SHSAT Math Quiz: Fractions Decimals And Percents
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Fractions Decimals And PercentsQuestion 1 of 20

If p=0.005p=0.005, which of the following is equal to pp expressed as a fraction in simplest form?

120\dfrac{1}{20}
1200\dfrac{1}{200}
51000\dfrac{5}{1000}
5100\dfrac{5}{100}
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SHSAT Math Quiz

SHSAT Math Quiz: Fractions Decimals And Percents

Practice Fractions Decimals And Percents in SHSAT Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Fractions Decimals And Percents, giving you a quick way to practice the rules, question types, and explanations that matter most for SHSAT Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

If p=0.005p=0.005, which of the following is equal to pp expressed as a fraction in simplest form?

  1. 120\dfrac{1}{20}
  2. 1200\dfrac{1}{200} (correct answer)
  3. 51000\dfrac{5}{1000}
  4. 5100\dfrac{5}{100}
Explanation: When you encounter a decimal that needs to be converted to a fraction, the key is understanding place value. Each decimal place represents a power of 10 in the denominator. The decimal 0.0050.005 has three decimal places, so it equals 51000\frac{5}{1000} (5 in the thousandths place). However, this fraction isn't in simplest form yet. To simplify, you need to find the greatest common factor of 5 and 1000. Since 1000=5×2001000 = 5 \times 200, you can divide both numerator and denominator by 5: 51000=5÷51000÷5=1200\frac{5}{1000} = \frac{5 ÷ 5}{1000 ÷ 5} = \frac{1}{200}. This confirms answer choice B is correct. Looking at the wrong answers: Choice A gives 120=0.05\frac{1}{20} = 0.05, which is ten times larger than our target value—a common error when miscounting decimal places. Choice C is 51000\frac{5}{1000}, which equals 0.0050.005 but isn't simplified. While mathematically equivalent to the correct answer, it's not in "simplest form" as the question requires. Choice D gives 5100=0.05\frac{5}{100} = 0.05, again ten times too large. Remember this pattern: to convert a decimal to a fraction, use the place value to determine your denominator (tenths = 10, hundredths = 100, thousandths = 1000), then simplify by finding common factors. Always check that your final fraction is fully reduced—the SHSAT often includes the unreduced form as a distractor.

Question 2

Which fraction equals 87.5%87.5\%?

  1. 78\dfrac{7}{8} (correct answer)
  2. 56\dfrac{5}{6}
  3. 1316\dfrac{13}{16}
  4. 45\dfrac{4}{5}
Explanation: When you encounter percentage-to-fraction conversion problems, the key is to convert the percentage to a decimal first, then find the equivalent fraction in simplest form. To solve this, start by converting 87.5%87.5\% to a decimal: 87.5%=87.5÷100=0.87587.5\% = 87.5 ÷ 100 = 0.875. Now you need to express 0.8750.875 as a fraction. Since there are three decimal places, write it as 8751000\frac{875}{1000}. To simplify, find the greatest common factor of 875 and 1000. Both are divisible by 125: 875÷1251000÷125=78\frac{875 ÷ 125}{1000 ÷ 125} = \frac{7}{8}. You can verify this by dividing: 7÷8=0.875=87.5%7 ÷ 8 = 0.875 = 87.5\%. Looking at the wrong answers: Choice B, 56\frac{5}{6}, equals approximately 0.8330.833 or 83.3%83.3\% - close to our target but not exact. Choice C, 1316\frac{13}{16}, equals 0.81250.8125 or 81.25%81.25\% - this is exactly 6.256.25 percentage points too low. Choice D, 45\frac{4}{5}, equals 0.80.8 or 80%80\% - significantly lower than 87.5%87.5\%. Study tip: Memorize common fraction-percentage equivalents like 18=12.5%\frac{1}{8} = 12.5\%, 14=25%\frac{1}{4} = 25\%, 38=37.5%\frac{3}{8} = 37.5\%, 12=50%\frac{1}{2} = 50\%, 58=62.5%\frac{5}{8} = 62.5\%, 34=75%\frac{3}{4} = 75\%, and 78=87.5%\frac{7}{8} = 87.5\%. Recognizing these patterns will save you valuable time on the SHSAT.

Question 3

A recipe calls for 0.60.6 cup of oil. What fraction of a cup is this amount?

  1. 35\dfrac{3}{5} (correct answer)
  2. 610\dfrac{6}{10}
  3. 23\dfrac{2}{3}
  4. 58\dfrac{5}{8}
Explanation: When you encounter a decimal that needs to be converted to a fraction, you're working with place value concepts. The key is recognizing what each decimal place represents and then simplifying the resulting fraction. The decimal 0.60.6 means "6 tenths" because the 6 is in the tenths place. This directly translates to the fraction 610\frac{6}{10}. However, fractions should always be expressed in lowest terms, so you need to find the greatest common factor of 6 and 10. Both numbers are divisible by 2: 610=6÷210÷2=35\frac{6}{10} = \frac{6 ÷ 2}{10 ÷ 2} = \frac{3}{5}. Therefore, choice A is correct. Let's examine why the other options are incorrect. Choice B gives 610\frac{6}{10}, which equals 0.60.6 but isn't simplified to lowest terms. While mathematically equivalent to the correct answer, this isn't the best form. Choice C shows 23\frac{2}{3}, which equals approximately 0.6670.667 when converted to a decimal—close to 0.60.6 but not exact. Choice D presents 58\frac{5}{8}, which equals 0.6250.625 as a decimal, again close but not equivalent to 0.60.6. Remember that when converting decimals to fractions, always check if your answer can be simplified. The SHSAT often includes the unsimplified fraction as a distractor, so reducing to lowest terms is essential. Also, be careful not to choose fractions that are "close" to the decimal value—they must be exactly equivalent.

Question 4

A survey shows that 0.830.83 of students prefer option A. What is this as a percent, rounded to the nearest whole percent?

  1. 8%
  2. 17%
  3. 83% (correct answer)
  4. 83.3%
Explanation: When you see a decimal that needs to be converted to a percentage, remember that "percent" literally means "per hundred." To convert any decimal to a percentage, you multiply by 100 and add the percent symbol. Starting with 0.830.83, you multiply by 100: 0.83×100=830.83 \times 100 = 83. This gives you 83%, which rounds to 83% since there are no additional decimal places to consider. Looking at the wrong answers: Choice A (8%) represents a major conceptual error—perhaps confusing 0.83 with 0.08 or misunderstanding place value entirely. Choice B (17%) might come from incorrectly thinking 0.83 means "83 out of 100 are NOT option A" and calculating 100 - 83 = 17, but that's not what the decimal represents. Choice D (83.3%) suggests confusion about the rounding process—since 0.83 converted directly gives exactly 83%, there's no need for decimal places, and certainly no reason to add a ".3" that doesn't exist in the original number. The key insight is that 0.83 already represents 83 hundredths, so when you convert to percentage form (which is also based on hundredths), you get exactly 83%. Study tip: When converting decimals to percentages on the SHSAT, always multiply by 100 first, then apply any rounding. Don't overthink it—if you see 0.83, that's 83 hundredths, which is 83%.

Question 5

Which of the following represents the largest value?

  1. 6212%62\frac{1}{2}\%
  2. 712+0.08\frac{7}{12} + 0.08 (correct answer)
  3. 0.63‾0.\overline{63}
  4. 58\frac{5}{8}
Explanation: When comparing values in different formats—percentages, decimals, fractions, and mixed expressions—convert everything to the same format to make accurate comparisons. Let's convert all options to decimals. For choice A, 6212%=62.5%=0.62562\frac{1}{2}\% = 62.5\% = 0.625. For choice B, we need 712+0.08\frac{7}{12} + 0.08. To convert 712\frac{7}{12} to a decimal, divide: 7÷12=0.5833‾7 \div 12 = 0.583\overline{3}. So 712+0.08=0.5833‾+0.08=0.6633‾\frac{7}{12} + 0.08 = 0.583\overline{3} + 0.08 = 0.663\overline{3}. For choice C, 0.63‾0.\overline{63} means the digits 63 repeat infinitely: 0.636363...0.636363... This equals 0.6363‾0.63\overline{63}. For choice D, 58=5÷8=0.625\frac{5}{8} = 5 \div 8 = 0.625. Comparing our decimal values:
  • A: 0.6250.625
  • B: 0.6633‾0.663\overline{3}
  • C: 0.6363‾0.63\overline{63}
  • D: 0.6250.625
Choice B gives us approximately 0.6630.663, which is the largest value. Choice A is incorrect because 0.625<0.6630.625 < 0.663. Choice C is wrong because 0.636...<0.6630.636... < 0.663—don't confuse the repeating pattern with the actual value. Choice D is incorrect because 0.6250.625 equals choice A and is smaller than B. Strategy tip: When comparing mixed formats, convert everything to decimals first. For fractions, use long division, and remember that repeating decimals like 0.63‾0.\overline{63} mean the entire sequence repeats, not just individual digits.

Question 6

The decimal 2.1252.125 is what percent?

  1. 2.125%
  2. 21.25%
  3. 212.5% (correct answer)
  4. 2125%
Explanation: This question tests your understanding of converting decimals to percentages, a fundamental skill that appears frequently on the SHSAT. To convert any decimal to a percentage, you multiply by 100 and add the percent symbol. This works because "percent" literally means "per hundred," so you're expressing how many parts per 100 the decimal represents. For 2.1252.125, multiply by 100: 2.125×100=212.52.125 \times 100 = 212.5. Therefore, 2.125=212.5%2.125 = 212.5\%, making choice C correct. Let's examine why the other options are wrong. Choice A (2.125%) represents a common misconception where students simply add the percent symbol without converting. This would actually equal 0.021250.02125 as a decimal, not 2.1252.125. Choice B (21.25%) comes from multiplying by 10 instead of 100—students sometimes forget that percentage conversion requires multiplying by 100, not 10. Choice D (2125%) results from multiplying by 1000 instead of 100, perhaps from confusion about decimal place movement. Remember this pattern: when converting decimals to percentages, always multiply by 100 and move the decimal point two places to the right. A decimal greater than 1 will always convert to a percentage greater than 100%, which might seem unusual but is mathematically correct. On the SHSAT, don't let large percentages throw you off—trust your conversion process.

Question 7

Which of the following represents 0.333…0.333\ldots (the repetend 3) as a fraction?

  1. 12\dfrac{1}{2}
  2. 13\dfrac{1}{3} (correct answer)
  3. 310\dfrac{3}{10}
  4. 33100\dfrac{33}{100}
Explanation: When you encounter a repeating decimal like 0.333…0.333\ldots, you're dealing with a rational number that can be expressed as a fraction. The key is recognizing common decimal-to-fraction conversions or using algebraic methods to find the exact fraction. Let's use algebra to convert 0.333…0.333\ldots to a fraction. Let x=0.333…x = 0.333\ldots. Since the digit 3 repeats infinitely, we can multiply both sides by 10: 10x=3.333…10x = 3.333\ldots. Now subtract the original equation: 10x−x=3.333…−0.333…10x - x = 3.333\ldots - 0.333\ldots, which gives us 9x=39x = 3. Solving for xx: x=39=13x = \frac{3}{9} = \frac{1}{3}. We can verify this by dividing: 1÷3=0.333…1 ÷ 3 = 0.333\ldots Looking at the wrong answers: Choice A (12\frac{1}{2}) equals 0.5, which is clearly different from our repeating decimal. Choice C (310\frac{3}{10}) equals 0.3 exactly, not 0.333…0.333\ldots — this represents a terminating decimal with just one 3 after the decimal point. Choice D (33100\frac{33}{100}) equals 0.33, which has exactly two 3's after the decimal point but doesn't continue infinitely. The correct answer is B: 13\frac{1}{3}. Study tip: Memorize that 13=0.333…\frac{1}{3} = 0.333\ldots and 23=0.666…\frac{2}{3} = 0.666\ldots — these are among the most common repeating decimals on standardized tests. Also remember that any fraction with a denominator containing only factors of 2 and 5 will terminate, while others typically repeat.

Question 8

What decimal is equivalent to 4512%45\dfrac{1}{2}\%?

  1. 0.455 (correct answer)
  2. 4.55
  3. 0.452
  4. 0.4555
Explanation: When you encounter a mixed number percentage like 4512%45\dfrac{1}{2}\%, you need to convert it to decimal form through a two-step process: first convert the mixed number to an improper fraction or decimal, then convert the percentage to a decimal. Start by converting 4512%45\dfrac{1}{2}\% to a decimal percentage. The fraction 12=0.5\dfrac{1}{2} = 0.5, so 4512%=45.5%45\dfrac{1}{2}\% = 45.5\%. Now convert this percentage to a decimal by dividing by 100 (or moving the decimal point two places left): 45.5%=45.5100=0.45545.5\% = \frac{45.5}{100} = 0.455. Looking at the wrong answers: Choice B (4.55) represents a common error where you forgot to convert from percentage to decimal—this would be your answer if you stopped at 45.5% without dividing by 100. Choice C (0.452) might result from incorrectly converting 12\dfrac{1}{2} to 0.02 instead of 0.5, perhaps confusing it with 150\dfrac{1}{50}. Choice D (0.4555) could come from misreading the mixed number or making a calculation error during conversion. The correct answer is A (0.455). Strategy tip: When converting mixed number percentages, always convert the fractional part to a decimal first, then treat it as a regular percentage. Remember that converting any percentage to decimal means dividing by 100—a step that's easy to forget when you're focused on the mixed number conversion.

Question 9

A recipe calls for 1381\frac{3}{8} cups of flour, but Maria only has a measuring cup marked in tenths. What decimal amount should she measure?

  1. 1.3 cups
  2. 1.35 cups
  3. 1.375 cups (correct answer)
  4. 1.38 cups
Explanation: Converting the mixed number: 1 3/8 = 1 + 3/8. To convert 3/8 to decimal: 3 ÷ 8 = 0.375. Therefore, 1 3/8 = 1.375 cups. Choice A incorrectly converts 3/8 as 0.3. Choice B might result from incorrectly thinking 3/8 = 35/100. Choice D rounds 1.375 to the nearest hundredth incorrectly.

Question 10

In a survey, 0.450.45 of students prefer math, 25\frac{2}{5} prefer science, and the rest prefer English. What percent of students prefer English?

  1. 15% (correct answer)
  2. 25%
  3. 35%
  4. 85%
Explanation: First convert all to the same form. Math: 0.45 = 45%. Science: 2/5 = 0.40 = 40%. Total for math and science: 45% + 40% = 85%. Since all students must sum to 100%, English: 100% - 85% = 15%. Choice B might come from incorrectly calculating 2/5 as 25%. Choice C could result from calculation errors. Choice D gives the combined percent for math and science instead of English.

Question 11

A basketball player makes 35\frac{3}{5} of her free throws in the first half and 6623%66\frac{2}{3}\% in the second half. If she attempted the same number of free throws in each half, what fraction of all her free throws did she make?

  1. 23\frac{2}{3}
  2. 1930\frac{19}{30} (correct answer)
  3. 710\frac{7}{10}
  4. 34\frac{3}{4}
Explanation: When you encounter problems involving fractions and percentages across different time periods or groups, you need to find a common way to express all the rates, then calculate the overall average. First, convert the percentage to a fraction to work with consistent units. 6623%=6623÷100=2003÷100=200300=2366\frac{2}{3}\% = 66\frac{2}{3} \div 100 = \frac{200}{3} \div 100 = \frac{200}{300} = \frac{2}{3} Since she attempted the same number of free throws in each half, you can use any convenient number. Let's say she attempted 15 free throws per half (chosen because it's divisible by both denominators). First half: 35×15=9\frac{3}{5} \times 15 = 9 free throws made Second half: 23×15=10\frac{2}{3} \times 15 = 10 free throws made Total made: 9+10=199 + 10 = 19 Total attempted: 15+15=3015 + 15 = 30 Overall fraction: 1930\frac{19}{30} Choice A (23\frac{2}{3}) incorrectly assumes you just average the two fractions: 35+232\frac{\frac{3}{5} + \frac{2}{3}}{2}, but this ignores that the fractions represent rates, not totals. Choice C (710\frac{7}{10}) might result from incorrectly converting the percentage or adding the numerators and denominators separately. Choice D (34\frac{3}{4}) could come from rounding 6623%66\frac{2}{3}\% to 67%67\% and then making calculation errors. Remember: when combining rates or percentages from equal-sized groups, convert everything to the same format first, then calculate the total outcomes divided by total attempts rather than averaging the rates themselves.

Question 12

Which fraction is equivalent to the decimal 0.3750.375 when written in simplest form?

  1. 38\dfrac{3}{8} (correct answer)
  2. 37100\dfrac{37}{100}
  3. 1532\dfrac{15}{32}
  4. 75200\dfrac{75}{200}
Explanation: When you encounter a decimal-to-fraction conversion problem, you need to express the decimal as a fraction and then simplify it to lowest terms. To convert 0.3750.375 to a fraction, recognize that it has three decimal places, so you can write it as 3751000\frac{375}{1000}. Now you need to simplify by finding the greatest common factor (GCF) of 375 and 1000. Finding factors: 375=3×125=3×53375 = 3 \times 125 = 3 \times 5^3 and 1000=8×125=23×531000 = 8 \times 125 = 2^3 \times 5^3. The GCF is 125125, so 3751000=375÷1251000÷125=38\frac{375}{1000} = \frac{375 ÷ 125}{1000 ÷ 125} = \frac{3}{8}. Let's check each answer choice: A) 38\frac{3}{8} is correct. Converting back: 3÷8=0.3753 ÷ 8 = 0.375 ✓ B) 37100=0.37\frac{37}{100} = 0.37, which rounds the original decimal and loses the final digit. This represents a common error of misreading the decimal. C) 1532\frac{15}{32} equals 0.468750.46875 when converted to decimal form, which is completely different from our target value. D) 75200\frac{75}{200} can be simplified to 38\frac{3}{8} (dividing both numerator and denominator by 25), so it's actually equivalent to choice A, but the question asks for simplest form. This tests whether you recognize that fractions should be fully reduced. Remember: Always simplify fractions to lowest terms, and you can verify your answer by converting back to decimal form using long division.

Question 13

Express 4.6%4.6\% as a decimal.

  1. 0.046 (correct answer)
  2. 0.46
  3. 4.6
  4. 46
Explanation: When you encounter a percentage-to-decimal conversion problem, remember that "percent" literally means "per hundred," so you're working with parts out of 100. To convert any percentage to a decimal, divide by 100 (or equivalently, move the decimal point two places to the left). For 4.6%4.6\%, you have 4.6÷100=0.0464.6 ÷ 100 = 0.046. Think of it this way: 4.6%4.6\% means 4.6100\frac{4.6}{100}, which equals 0.0460.046. Looking at the answer choices, option A gives us 0.0460.046, which is correct. Option B (0.460.46) represents what you'd get if you only moved the decimal point one place to the left instead of two—this is the result of dividing by 10 instead of 100. Option C (4.64.6) is just the original number without any conversion; this would be correct if the question asked you to remove the percent symbol but not convert to decimal form. Option D (4646) comes from multiplying by 10 instead of dividing by 100, which reverses the operation entirely. You can verify this makes sense: 0.0460.046 as a percentage would be 0.046×100=4.6%0.046 × 100 = 4.6\%, confirming our answer. Study tip: Always remember the "move two places left" rule for percent-to-decimal conversion. If you're unsure, think of common examples: 50%=0.5050\% = 0.50 and 25%=0.2525\% = 0.25. This pattern will help you avoid the common trap of only moving one decimal place.

Question 14

Which of the following is NOT equivalent to 34\dfrac{3}{4}?

  1. 0.75
  2. 75%
  3. 68\dfrac{6}{8}
  4. 0.075 (correct answer)
Explanation: This question tests your ability to convert between different representations of the same value: fractions, decimals, and percentages. When you encounter equivalent forms problems, systematically convert everything to the same format to compare. Let's convert 34\frac{3}{4} to decimal form by dividing: 3÷4=0.753 \div 4 = 0.75. Now we can check each option against this decimal value. Choice A gives us 0.75, which matches our conversion exactly. Choice B shows 75%, and since percent means "per hundred," we convert: 75%=75100=0.7575\% = \frac{75}{100} = 0.75. Choice C presents 68\frac{6}{8}, which simplifies when we divide both numerator and denominator by 2: 6÷28÷2=34\frac{6 \div 2}{8 \div 2} = \frac{3}{4}. Alternatively, converting to decimal: 6÷8=0.756 \div 8 = 0.75. Choice D gives us 0.075, which equals 751000\frac{75}{1000} or 340\frac{3}{40} when simplified. This is much smaller than 34\frac{3}{4} and represents a common decimal place error. The answer is D because 0.075 is one-tenth the value of 0.75. This mistake often occurs when students misplace the decimal point or confuse 75% with 0.075 instead of 0.75. Study tip: When working with equivalent forms, always convert everything to the same format—preferably decimals since they're easiest to compare. Watch out for decimal place errors, especially when converting between percentages and decimals.

Question 15

A string is cut so that 12.5%12.5\% of its original length remains. Express this remaining fraction of the original length as a fraction in simplest form.

  1. 16\dfrac{1}{6}
  2. 18\dfrac{1}{8} (correct answer)
  3. 14\dfrac{1}{4}
  4. 12\dfrac{1}{2}
Explanation: When you encounter percentage-to-fraction conversion problems, you're working with the relationship between decimal representations and their fractional equivalents. The key is converting the percentage to a decimal first, then finding the simplest fractional form. To convert 12.5%12.5\% to a fraction, start by writing it as a decimal: 12.5%=0.12512.5\% = 0.125. Now convert this decimal to a fraction by recognizing that 0.125=12510000.125 = \frac{125}{1000}. To simplify, find the greatest common divisor of 125 and 1000. Since 125=53125 = 5^3 and 1000=23×531000 = 2^3 \times 5^3, the GCD is 53=1255^3 = 125. Dividing both numerator and denominator by 125 gives us 125÷1251000÷125=18\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}. Looking at the wrong answers: Choice A (16\frac{1}{6}) equals approximately 16.67%16.67\%, which is significantly larger than 12.5%12.5\%. Choice C (14\frac{1}{4}) equals 25%25\%, exactly double what we need. Choice D (12\frac{1}{2}) equals 50%50\%, which is four times too large. The correct answer is B: 18\frac{1}{8}. Remember that 12.5%12.5\% is exactly half of 25%25\% (which equals 14\frac{1}{4}), so the answer should be half of 14\frac{1}{4}, giving you 18\frac{1}{8}. This relationship can serve as a quick check: when you halve a percentage, you double the denominator of its fractional equivalent.

Question 16

Which of the following represents 250%250\% as a decimal?

  1. 2.5 (correct answer)
  2. 0.25
  3. 25
  4. 0.025
Explanation: When you encounter percentage-to-decimal conversion problems, remember that "percent" literally means "per hundred," so you're working with parts of 100. To convert any percentage to a decimal, divide by 100 (or equivalently, move the decimal point two places to the left). For 250%250\%, you calculate: 250÷100=2.5250 ÷ 100 = 2.5. You can also think of this as moving the decimal point in 250 two places left: from 250.250. to 2.502.50 or simply 2.52.5. Let's examine why the other choices represent common conversion errors. Choice B (0.250.25) would be correct if you were converting 25%25\% to a decimal, not 250%250\%. This suggests confusion about place value or accidentally dropping a zero. Choice C (2525) comes from the opposite mistake—multiplying by 100 instead of dividing, which would convert a decimal to a percentage rather than the reverse. Choice D (0.0250.025) results from moving the decimal point too far left (three places instead of two), treating the conversion as if you were dividing by 1000. The correct answer is A (2.52.5). Remember this key insight: percentages greater than 100%100\% always convert to decimals greater than 1. Since 250%250\% represents "250 parts per 100," or "2.5 times the whole," your decimal answer should exceed 1. This reasoning can help you eliminate obviously incorrect choices and check your work on percentage conversion problems.

Question 17

Which percent is equivalent to 1120\dfrac{11}{20}?

  1. 45%
  2. 50%
  3. 55% (correct answer)
  4. 60%
Explanation: Converting fractions to percentages is a fundamental skill that appears frequently on the SHSAT. When you see a fraction that needs to be converted to a percent, you have two main approaches: convert to a decimal first, or find an equivalent fraction with 100 in the denominator. To convert 1120\frac{11}{20} to a percentage, let's use the decimal method. Divide 11 by 20: 11÷20=0.5511 ÷ 20 = 0.55. To convert any decimal to a percentage, multiply by 100 (or move the decimal point two places right): 0.55×100=55%0.55 × 100 = 55\%. Alternatively, you can find an equivalent fraction with 100 in the denominator. Since 20×5=10020 × 5 = 100, multiply both numerator and denominator by 5: 1120=11×520×5=55100=55%\frac{11}{20} = \frac{11 × 5}{20 × 5} = \frac{55}{100} = 55\%. Looking at the wrong answers: Choice A (45%) would result from incorrectly calculating 920\frac{9}{20} instead of 1120\frac{11}{20}. Choice B (50%) represents 1020\frac{10}{20} or 12\frac{1}{2}, which is close but not our fraction. Choice D (60%) would come from 1220\frac{12}{20} or 35\frac{3}{5}, again close but incorrect. The correct answer is C) 55%. Strategy tip: Memorize common fraction-to-percent conversions like 14=25%\frac{1}{4} = 25\%, 12=50%\frac{1}{2} = 50\%, and 34=75%\frac{3}{4} = 75\%. For fractions with denominators of 20, remember that each unit represents 5%, so 1120=11×5%=55%\frac{11}{20} = 11 × 5\% = 55\%.

Question 18

Which decimal is equal to 316\dfrac{3}{16}?

  1. 0.18
  2. 0.1875 (correct answer)
  3. 0.1818
  4. 0.2
Explanation: When you need to convert a fraction to a decimal, you have two main approaches: long division or recognizing patterns with common denominators. To convert 316\frac{3}{16} to a decimal, divide 3 by 16 using long division. Set up 3.0000 ÷ 16. Since 16 doesn't go into 3, move to 30. 16 goes into 30 once (16 × 1 = 16), leaving a remainder of 14. Bring down the next 0 to get 140. 16 goes into 140 eight times (16 × 8 = 128), leaving remainder 12. Continue: 16 goes into 120 seven times (16 × 7 = 112), remainder 8. Finally, 16 goes into 80 exactly 5 times. This gives you 0.1875, confirming that answer B is correct. Looking at the wrong answers: A) 0.18 results from stopping the division too early after getting 0.1 and roughly estimating the remainder. C) 0.1818 suggests confusion with a repeating decimal pattern, possibly thinking of fractions like 211\frac{2}{11}. D) 0.2 comes from the approximation 316≈315=0.2\frac{3}{16} ≈ \frac{3}{15} = 0.2, but this oversimplifies the actual denominator. Pro tip: Memorize decimal equivalents for sixteenths since they appear frequently on standardized tests. Key ones include 116=0.0625\frac{1}{16} = 0.0625, 316=0.1875\frac{3}{16} = 0.1875, and 516=0.3125\frac{5}{16} = 0.3125. Notice the pattern: sixteenths always end in .0625, .1875, .3125, .4375, etc. This can help you eliminate obviously wrong answers quickly.

Question 19

Express 7.27.2 as a percent.

  1. 0.72%
  2. 7.2%
  3. 72%
  4. 720% (correct answer)
Explanation: When you see a problem asking to express a number as a percent, you need to understand what "percent" means. Percent literally means "per hundred" or "out of 100." So expressing a number as a percent means showing how many parts out of 100 that number represents. To convert any number to a percent, multiply it by 100 and add the percent symbol. This is because you're finding how many hundredths the number contains. For 7.27.2, we calculate: 7.2×100=7207.2 \times 100 = 720, so 7.2=720%7.2 = 720\%. Think of it this way: 7.27.2 means 7.27.2 wholes, which is the same as 720720 hundredths, or 720%720\%. Choice A (0.72%0.72\%) represents what you'd get if you divided 7.27.2 by 100100 instead of multiplying - this is the opposite of the correct operation. Choice B (7.2%7.2\%) is the trap of simply adding a percent sign without converting. This would only be correct if the original number were 0.0720.072. Choice C (72%72\%) results from multiplying by 1010 instead of 100100, missing a factor of 1010. Remember this pattern: to convert a decimal or whole number to a percent, always multiply by 100100. Moving the decimal point two places to the right is the same operation. Numbers greater than 11 will always give you percentages greater than 100%100\%, which is perfectly normal - it just means more than one whole.

Question 20

Convert 135%135\% to a mixed number.

  1. 1351001\dfrac{35}{100}
  2. 13510001\dfrac{35}{1000}
  3. 17201\dfrac{7}{20} (correct answer)
  4. 1351\dfrac{3}{5}
Explanation: Converting percentages to mixed numbers requires understanding that a percentage over 100% represents a value greater than 1 whole. When you see 135%, think of it as "135 out of 100" or 135100\frac{135}{100}. To convert 135%135\% to a mixed number, first write it as an improper fraction: 135100\frac{135}{100}. Since 135 is greater than 100, this fraction is greater than 1, so it can be written as a mixed number. Divide 135 by 100: 135÷100=1135 ÷ 100 = 1 with remainder 3535. This gives you 1351001\frac{35}{100}. However, you're not finished yet. Always reduce fractions to lowest terms by finding the greatest common factor (GCF) of the numerator and denominator. The GCF of 35 and 100 is 5, since 35=5×735 = 5 × 7 and 100=5×20100 = 5 × 20. Dividing both by 5: 35100=35÷5100÷5=720\frac{35}{100} = \frac{35÷5}{100÷5} = \frac{7}{20}. Therefore, 135%=1720135\% = 1\frac{7}{20}, which is choice C. Choice A gives 1351001\frac{35}{100} but fails to reduce the fraction to lowest terms. Choice B shows 13510001\frac{35}{1000}, which incorrectly uses 1000 as the denominator instead of 100. Choice D gives 1351\frac{3}{5}, which would equal 1601001\frac{60}{100} or 160%, not 135%. Always remember to reduce fractions to their simplest form as the final step when converting percentages to mixed numbers. The SHSAT consistently expects answers in lowest terms.