Comparing Rational Numbers - ISEE Upper Level Quantitative Reasoning

1. A quality control inspector finds that $\frac{3}{8}$ of products from Machine A, $37.6\%$ of products from Machine B, and $0.374$ of products from Machine C meet specifications. Which machine has the highest rate of products meeting specifications?
   Answer: Machine B, because $37.6\% = 0.376$ which exceeds the other rates When comparing rates or percentages given in different formats, you need to convert them all to the same form to make an accurate comparison. Let's convert all three rates to decimals. Machine A produces $\frac{3}{8}$ products meeting specifications. To convert this fraction: $\frac{3}{8} = 3 ÷ 8 = 0.375$. Machine B has a rate of $37.6\%$, which converts to $37.6 ÷ 100 = 0.376$. Machine C already gives us the decimal: $0.374$. Now we can compare: Machine A = 0.375, Machine B = 0.376, Machine C = 0.374. Machine B has the highest rate at 0.376. Choice A incorrectly claims Machine A has the highest rate. While it correctly converts $\frac{3}{8} = 0.375$, this value is actually less than Machine B's 0.376. Choice C makes a fundamental error by suggesting 0.374 is the largest when compared directly—this shows a misunderstanding of decimal place values, as 0.374 is actually the smallest of the three. Choice D incorrectly states that Machines A and C are tied, when their rates are clearly different (0.375 vs. 0.374), and both are lower than Machine B's rate. The correct answer is B because Machine B's rate of 0.376 exceeds both other machines. Strategy tip: Always convert different formats (fractions, percentages, decimals) to the same form before comparing. When working with decimals, compare digit by digit from left to right—the first position where digits differ determines which number is larger.
2. Three friends are comparing their quiz scores. Anna scored $\frac{17}{20}$, Ben scored $84.5\%$, and Carol scored $0.847$. If they want to arrange their scores from lowest to highest, what is the correct order?
   Answer: Ben, Carol, Anna Convert every score to a decimal. Anna: $\frac{17}{20} = 0.85$. Ben: $84.5\% = 0.845$. Carol: $0.847$. Compare to the thousandths place by writing Anna's score as 0.850: $0.845 < 0.847 < 0.850$. From lowest to highest, the order is Ben, Carol, Anna. Ben, Anna, Carol puts Anna below Carol, which happens when 0.85 is read as smaller than 0.847 because it has fewer digits. Anna, Ben, Carol puts Anna lowest even though her score is the highest. Carol, Ben, Anna treats 0.847 as smaller than 0.845; the hundredths match, so compare the thousandths: 7 is greater than 5.
3. A student claims that $\frac{7}{15}$ is greater than $0.4\overline{7}$ because "7 is greater than 4." Which of the following best explains why this reasoning is incorrect?
   Answer: Converting $\frac{7}{15}$ to decimal form gives $0.4\overline{6}$, which is less than $0.4\overline{7}$ When comparing fractions and decimals, you can't simply compare individual digits without considering place value and the actual numerical values. The student's error demonstrates a fundamental misunderstanding of how decimal comparison works. To properly compare these numbers, you need to convert them to the same form. Let's convert $\frac{7}{15}$ to decimal form by dividing: $7 ÷ 15 = 0.4666...$ or $0.4\overline{6}$. Now you can accurately compare $0.4\overline{6}$ with $0.4\overline{7}$. Since both have the same whole and tenths place (0.4), you compare the hundredths place: 6 versus 7. Since 6 < 7, we have $0.4\overline{6} < 0.4\overline{7}$, meaning $\frac{7}{15} < 0.4\overline{7}$. This shows the student's conclusion was wrong, and choice B correctly identifies both the proper decimal conversion and the accurate comparison. Choice A incorrectly suggests ignoring the repeating decimal, which changes the value entirely. Choice C unnecessarily complicates the problem—percentages don't make comparison easier here. Choice D claims the student's conclusion was correct, but as we've shown, $\frac{7}{15}$ is actually less than $0.4\overline{7}$. Study tip: When comparing fractions and decimals, always convert to the same form first. Never compare individual digits across different place values—the positional value matters more than the digit itself. Practice converting common fractions to decimals so you can make these comparisons quickly and accurately.
4. If $x = \frac{13}{30}$ and $y = 43.\overline{3}\%$, which statement about the relationship between $x$ and $y$ is true?
   Answer: $x = y$ because both expressions represent the same rational number When comparing fractions and percentages, you need to convert them to the same form to make an accurate comparison. This question tests your ability to work with repeating decimals and recognize equivalent representations of rational numbers. Let's convert both values to see their relationship. First, convert $x = \frac{13}{30}$ to a decimal by dividing: $13 ÷ 30 = 0.4\overline{3}$ (where the 3 repeats infinitely). Now convert $y = 43.\overline{3}\%$ to decimal form by dividing by 100: $43.\overline{3} ÷ 100 = 0.4\overline{3}$. Since both equal $0.4\overline{3}$, we have $x = y$. You can also verify this by converting the percentage to a fraction. Since $43.\overline{3} = 43\frac{1}{3} = \frac{130}{3}$, we get $43.\overline{3}\% = \frac{130/3}{100} = \frac{130}{300} = \frac{13}{30}$, which equals $x$. Choice A is wrong because the size relationship between numbers doesn't depend on their format—fractions aren't inherently larger than percentages. Choice B incorrectly states that $x < y$ even while correctly noting they're equal when converted. Choice D makes a calculation error by approximating $43.\overline{3}\%$ as 0.434 instead of recognizing that $43.\overline{3} = 43\frac{1}{3}$ exactly. When working with repeating decimals on standardized tests, look for patterns involving fractions with denominators like 3, 6, 9, or 30. Converting $\overline{3}$ patterns to fractions with 3 in the denominator often reveals the exact relationship.
5. A meteorologist reports that the probability of rain is $\frac{7}{20}$ on Monday, $35.2\%$ on Tuesday, and $0.348$ on Wednesday. On which day is rain most likely?
   Answer: Tuesday, because $35.2\% = 0.352$ which is the highest probability When comparing probabilities given in different formats, you need to convert everything to the same format to make accurate comparisons. Probabilities can be expressed as fractions, percentages, or decimals, but they all represent the same underlying concept. Let's convert all three probabilities to decimals. For Monday: $\frac{7}{20} = 7 \div 20 = 0.35$. For Tuesday: $35.2\% = 35.2 \div 100 = 0.352$. Wednesday is already given as a decimal: $0.348$. Now we can easily compare: Monday = 0.35, Tuesday = 0.352, Wednesday = 0.348. Since 0.352 is the largest value, Tuesday has the highest probability of rain. Choice A incorrectly states that Monday has the highest probability. While the conversion $\frac{7}{20} = 0.35$ is correct, 0.35 is not the highest value among the three days. Choice C makes the error of assuming that 0.348 is the highest probability without properly comparing all three converted values. Choice D incorrectly claims that Monday and Wednesday have equal probabilities—they don't (0.35 ≠ 0.348)—and also incorrectly states these are higher than Tuesday's probability. The correct answer is B because Tuesday's probability of 0.352 is indeed the highest when all probabilities are expressed in decimal form. Study tip: Always convert different probability formats to the same form before comparing. Decimals are usually easiest for comparison since you can directly see which decimal is larger without additional calculation.
6. In a class election, candidate Alpha received $\frac{2}{5}$ of votes, candidate Beta received $39.8\%$ of votes, and candidate Gamma received $0.402$ of votes. Who won the election?
   Answer: Gamma, because $0.402 > 0.4 > 0.398$ when all votes are compared When comparing fractions, percentages, and decimals, you need to convert everything to the same format to determine which is largest. Let's convert all votes to decimals for easy comparison: - Alpha: $\frac{2}{5} = 0.400$ - Beta: $39.8\% = 0.398$ - Gamma: $0.402$ (already in decimal form) Now you can clearly see: $0.402 > 0.400 > 0.398$, making Gamma the winner with the highest vote share. Looking at the wrong answers: Choice A incorrectly claims $\frac{2}{5} = 0.4$ is the highest. While the conversion is correct, $0.4 = 0.400$, which is less than Gamma's $0.402$. Choice C suggests Beta has the largest share, but $39.8\% = 0.398$ is actually the smallest of the three values. Choice D claims Alpha and Gamma tied because their values are "approximately equal," but $0.400$ and $0.402$ are not equal—Gamma's lead of $0.002$ represents 0.2 percentage points, which could mean several votes in a real election. The correct answer is B because when you convert all three vote shares to comparable decimal form, Gamma's $0.402$ is indeed the largest. Strategy tip: When comparing mixed formats (fractions, percentages, decimals), always convert to the same format first. Decimals are usually easiest for comparison since you can line up place values directly.
7. Three athletes' success rates are recorded as $\frac{14}{25}$, $55.9\%$, and $0.56\overline{1}$. If they want to determine who has the best performance, what should they conclude?
   Answer: The athlete with $0.56\overline{1}$ has the best performance as it represents the highest rate When comparing rates given in different formats, you need to convert them all to the same form to make accurate comparisons. This question tests your ability to work with fractions, percentages, and repeating decimals. Let's convert all three rates to decimals for easy comparison. First, $\frac{14}{25} = \frac{14 \times 4}{25 \times 4} = \frac{56}{100} = 0.56$. Second, $55.9\% = 0.559$. Third, $0.56\overline{1}$ means the digit 1 repeats infinitely, so this equals $0.561111... = \frac{505}{900} = \frac{101}{180} \approx 0.5611$. Comparing these values: $0.559 < 0.56 < 0.5611$. The athlete with $0.56\overline{1}$ has the highest success rate, making choice C correct. Choice A is wrong because $\frac{14}{25} = 0.56 = 56\%$, not "exactly 56%" as something special, and it's not the highest rate anyway. Choice B is incorrect because $55.9\%$ is actually the lowest of the three rates, not exceeding the others. Choice D is wrong because these rates are meaningfully different—the gap between the highest and lowest is about 0.002, which represents a clear performance difference, not measurement error. Study tip: When comparing numbers in mixed formats on the ISEE, always convert to the same form first. Be especially careful with repeating decimals—the overline notation means those digits repeat forever, often making the value larger than it initially appears.
8. Three stores offer discounts: Store X gives $\frac{1}{8}$ off, Store Y gives $12.6\%$ off, and Store Z gives $0.124$ off the regular price. Which store offers the smallest discount?
   Answer: Store Z, because $0.124 < 0.125 < 0.126$ when all discounts are compared When comparing discounts given in different formats, you need to convert everything to the same form—either all decimals, all percentages, or all fractions—to make an accurate comparison. Let's convert all three discounts to decimals. Store X offers $\frac{1}{8}$ off, which equals $1 ÷ 8 = 0.125$. Store Y gives $12.6\%$ off, which converts to $12.6 ÷ 100 = 0.126$. Store Z offers $0.124$ off, which is already in decimal form. Now we can compare: $0.124 < 0.125 < 0.126$. Store Z offers the smallest discount at $0.124$, making choice B correct. Choice A incorrectly identifies Store X as having the smallest discount. While it correctly calculates that $\frac{1}{8} = 0.125$, it fails to properly compare this with the other values. Choice C makes an error in reasoning—it correctly converts $12.6\% = 0.126$ but then claims this larger value represents a smaller discount, confusing "greater than" with "smallest discount." Choice D incorrectly states that Stores X and Z offer equal discounts, when $0.125 ≠ 0.124$. Strategy tip: Always convert mixed formats to the same unit before comparing. Write out the decimal equivalents to three decimal places when dealing with percentages and fractions to avoid rounding errors. Remember that the smallest decimal represents the smallest discount amount.
9. In a survey about transportation preferences, $\frac{5}{12}$ chose cars, $41.\overline{6}\%$ chose public transit, and $0.41\overline{7}$ chose walking. Which transportation method was least preferred?
   Answer: Cars and public transit are tied for least preferred, both less than walking When comparing different number formats like fractions, percentages, and decimals, you need to convert everything to the same form to make accurate comparisons. Let's convert all three values to decimals. First, $\frac{5}{12} = 5 \div 12 = 0.41\overline{6}$ (where the 6 repeats). Next, $41.\overline{6}\% = 41.666...\% = 0.41\overline{6}$ as a decimal. Finally, walking is already given as $0.41\overline{7}$ (where the 7 repeats). Now we can compare: cars = $0.41\overline{6}$, public transit = $0.41\overline{6}$, and walking = $0.41\overline{7}$. Since $0.41\overline{7} > 0.41\overline{6}$, walking received the highest preference, while cars and public transit are tied for the lowest preference. Choice A incorrectly states that $\frac{5}{12}$ is the smallest value, but it's actually tied with public transit, not smaller. Choice B makes the same error, claiming public transit alone is smallest when it's tied with cars. Choice C confuses the question's logic—it correctly identifies that $0.41\overline{7}$ is largest but then incorrectly concludes this means it's least preferred, when the largest percentage actually indicates the most preferred option. Remember to always convert mixed number formats to the same form before comparing, and pay careful attention to repeating decimals—the difference between $0.41\overline{6}$ and $0.41\overline{7}$ is small but significant for determining order.
10. A student claims that $\frac{9}{20}$ is less than $44.9\%$ because "fractions are always smaller than percentages." What is wrong with this reasoning?
    Answer: The statement about fractions and percentages is false, and $\frac{9}{20} > 44.9\%$ When comparing fractions and percentages, you need to convert them to the same form to make an accurate comparison. The student's claim contains both a mathematical error and a flawed general rule. Let's convert $\frac{9}{20}$ to a percentage: $\frac{9}{20} = \frac{9 \times 5}{20 \times 5} = \frac{45}{100} = 45\%$. Since $45\% > 44.9\%$, the fraction is actually greater than the percentage, not less than it. The student's reasoning that "fractions are always smaller than percentages" is completely false. The numerical relationship between a fraction and a percentage depends on their actual values, not their forms. For example, $\frac{1}{2} = 50\%$ (equal), $\frac{3}{4} = 75\%$ (fraction represents a larger value than $60\%$), and $\frac{1}{10} = 10\%$ (fraction represents a smaller value than $25\%$). Looking at the answer choices: Choice A incorrectly states the reasoning is correct when it isn't. Choice B suggests you can't compare fractions and percentages, but you absolutely can after converting to a common form. Choice D agrees the comparison is correct ($\frac{9}{20} < 44.9\%$), which is mathematically wrong. Choice C correctly identifies both problems: the general statement about fractions and percentages is false, and $\frac{9}{20}$ is actually greater than $44.9\%$. Study tip: Always convert fractions and percentages to the same form before comparing. To convert a fraction to a percentage, multiply by 100 or find an equivalent fraction with denominator 100.
11. A student calculated that $\frac{7}{12} = 0.58\overline{3}$ and concluded that $\frac{7}{12} > 58\%$. Is this conclusion correct?
    Answer: Yes, because $0.58\overline{3} > 0.58$ and $58\% = 0.58$ To compare a fraction with a percent, write both as decimals. Dividing 7 by 12 gives $0.58333\ldots = 0.58\overline{3}$, so the student's conversion is correct. Next, $58\% = 0.58 = 0.58000\ldots$. Comparing digit by digit, the thousandths digit is 3 in $0.58\overline{3}$ and 0 in $0.58$, so $0.58\overline{3} > 0.58$. The conclusion $\frac{7}{12} > 58\%$ is correct. The claim that $58\% = 0.583$ misconverts the percent; 58% is exactly 0.58. Saying $\frac{7}{12} = 0.583$ exactly ignores that the 3 repeats forever. Rounding $0.58\overline{3}$ to 0.58 and calling the values equal throws away the very digits that make the fraction larger. Tip: never round before comparing; line up the decimal places and compare digit by digit.
12. A basketball player's free throw percentages for three games were $\frac{4}{5}$, $79.5\%$, and $0.802$. In which order should these be arranged from worst performance to best performance?
    Answer: $79.5\%$, $\frac{4}{5}$, $0.802$ When you encounter different representations of the same type of number (percentages, fractions, decimals), you need to convert them all to the same format to compare accurately. This question tests your ability to work flexibly with equivalent forms. To compare these free throw percentages, let's convert everything to decimals. Start with $\frac{4}{5}$: divide 4 by 5 to get 0.8. Next, convert 79.5% by dividing by 100: 79.5 ÷ 100 = 0.795. The third value, 0.802, is already in decimal form. Now you can easily compare: 0.795 < 0.8 < 0.802. Since the question asks for worst to best performance, the order is 79.5%, $\frac{4}{5}$, 0.802. Choice A is correct because it properly arranges the values from smallest (0.795) to largest (0.802). Choice B reverses the first two values, incorrectly placing $\frac{4}{5}$ (0.8) before 79.5% (0.795). Choice C correctly identifies 79.5% as the worst but then reverses the order of the other two values. Choice D completely reverses the correct order, treating the best performance (0.802) as the worst. Strategy tip: Always convert mixed number formats to the same type before comparing. Decimals are usually easiest to work with since you can compare them digit by digit from left to right. Remember that 0.8 = 0.800, so 0.802 > 0.800.
13. If $\frac{3}{8} = 0.375$ and $\frac{5}{12} = 0.41\overline{6}$, which statement correctly compares these numbers with $37\%$?
    Answer: $37\% < \frac{3}{8} < \frac{5}{12}$ When comparing fractions, decimals, and percentages, you need to convert everything to the same format first. The most efficient approach here is to convert all values to decimals. You're already given that $\frac{3}{8} = 0.375$ and $\frac{5}{12} = 0.41\overline{6}$ (which means 0.416666...). Now convert the percentage: $37\% = \frac{37}{100} = 0.37$. Arranging these decimals from smallest to largest: $0.37 < 0.375 < 0.41\overline{6}$. Converting back to the original forms: $37\% < \frac{3}{8} < \frac{5}{12}$, which matches answer choice B. Let's examine why the other choices are incorrect. Choice A suggests $\frac{3}{8} < 37\% < \frac{5}{12}$, but this would mean $0.375 < 0.37$, which is false since 0.375 is greater than 0.37. Choice C claims $\frac{5}{12} < 37\% < \frac{3}{8}$, placing the largest value (0.416...) as the smallest, which reverses the actual order. Choice D states $\frac{5}{12} < \frac{3}{8} < 37\%$, which would make 37% the largest value, but 0.37 is actually the smallest of the three. Remember this strategy: when comparing mixed formats (fractions, decimals, percentages), convert everything to decimals first. It's usually the fastest and least error-prone method. Also, be extra careful with decimal place values—0.37 versus 0.375 can be tricky to compare at first glance.
14. Which inequality correctly represents the relationship between $\frac{11}{24}$, $45.8\%$, and $0.4\overline{583}$?
    Answer: $45.8\% < \frac{11}{24} < 0.4\overline{583}$ When comparing numbers in different formats, you need to convert them all to the same form—typically decimals—to determine their relative sizes. Let's convert each number to decimal form. First, $45.8\% = 0.458$. Next, $\frac{11}{24}$: dividing 11 by 24 gives us $0.458\overline{3}$ (where the 3 repeats). Finally, $0.4\overline{583}$ means the digits 583 repeat infinitely: $0.4583583583...$ Now we can compare: - $45.8\% = 0.458$ - $\frac{11}{24} = 0.458\overline{3} = 0.458333...$ - $0.4\overline{583} = 0.4583583...$ Since $0.458 < 0.458333... < 0.4583583...$, we have $45.8\% < \frac{11}{24} < 0.4\overline{583}$. Choice A incorrectly places the repeating decimal as the smallest value, but $0.4583... > 0.458333...$ Choice B incorrectly ranks the percentage as smallest and the fraction as largest, missing that the fraction falls between the other two values. Choice D incorrectly places the fraction as the smallest value, but $\frac{11}{24} = 0.458333... > 0.458$. Study tip: When comparing mixed number formats, always convert to decimals first. Pay special attention to repeating decimals—calculate several decimal places to see the pattern clearly. The key is being methodical with your conversions rather than trying to estimate.
15. A student argues that $0.\overline{571428} = \frac{4}{7}$ and therefore $0.\overline{571428} > 57\%$. Is this argument valid?
    Answer: Yes, because $\frac{4}{7} = 0.\overline{571428}$ and this repeating decimal is greater than $0.57$ Check both parts of the argument: the conversion and the comparison. Dividing 4 by 7 gives $0.571428571428\ldots$, which is $0.\overline{571428}$, so the premise is true. Next, $57\% = 0.57 = 0.570000\ldots$. Comparing digit by digit, the thousandths digit is 1 in $0.\overline{571428}$ and 0 in $0.57$, so the repeating decimal is larger and the argument is valid. Rounding $\frac{4}{7}$ to 0.57 and calling the values equal throws away the digits that make the fraction larger. Denying that $0.\overline{571428} = \frac{4}{7}$ is wrong, since long division produces exactly that repeating block. Claiming $57\% > \frac{4}{7}$ reverses the comparison. Tip: compare decimals place by place without rounding first.
16. In a survey, $\frac{3}{7}$ of students preferred math, $42.9\%$ preferred science, and $0.428$ preferred English. Which subject was most preferred?
    Answer: Science, because $42.9\%$ is greater than both $\frac{3}{7}$ and $0.428$ When comparing quantities expressed in different formats—fractions, percentages, and decimals—you need to convert them all to the same format to make accurate comparisons. Let's convert all three values to decimals to compare them directly. For math: $\frac{3}{7} = 3 \div 7 = 0.428571...$ or approximately $0.429$. For science: $42.9\% = \frac{42.9}{100} = 0.429$. English is already given as $0.428$. Now we can compare: Math ≈ $0.429$, Science = $0.429$, and English = $0.428$. Science has the highest value at exactly $0.429$, making it the most preferred subject. Looking at the wrong answers: Choice A incorrectly assumes $\frac{3}{7}$ is largest without doing the conversion—this is a common trap when students don't convert to compare properly. Choice C makes no mathematical sense; it suggests that a smaller value indicates a measurement error, which has no basis in the problem. Choice D claims science and English are tied, but this ignores that $42.9\% = 0.429$ while English preference is $0.428$—these are clearly different values. The correct answer is B because $42.9\%$ equals $0.429$, which is greater than both $\frac{3}{7}$ (approximately $0.429$ but slightly less) and $0.428$. Study tip: Always convert fractions, decimals, and percentages to the same format before comparing. Decimals are usually the easiest common denominator for these comparisons.
17. A recipe calls for ingredients in the following proportions: flour $\frac{5}{8}$ cup, sugar $62.5\%$ cup, and butter $0.625$ cup. What can be concluded about these measurements?
    Answer: All three measurements represent exactly the same amount needed for the recipe When you encounter measurements given in different formats—fractions, percentages, and decimals—the key is converting them all to the same format to make accurate comparisons. Let's convert all three measurements to decimals. The flour measurement is $\frac{5}{8}$ cup. To convert this fraction, divide 5 by 8: $5 \div 8 = 0.625$. The sugar measurement is already given as a percentage: 62.5%. To convert a percentage to a decimal, divide by 100: $62.5 \div 100 = 0.625$. The butter measurement is already in decimal form: 0.625 cup. All three measurements equal 0.625 cups, meaning they represent exactly the same amount. Choice A is incorrect because once converted to the same format, all measurements are identical—they don't represent different amounts. Choice C incorrectly suggests that flour (0.625) and sugar (0.625) are equal while butter (0.625) is different, when in fact all three are equal. Choice D makes the opposite error, incorrectly claiming that sugar (0.625) and butter (0.625) are equal while flour (0.625) is different. The correct answer is B because all three ingredients require exactly the same amount: 0.625 cups each. Study tip: When comparing quantities in different formats, always convert everything to the same format first—usually decimals are easiest to work with. Remember that fractions, percentages, and decimals are just different ways of expressing the same values, and questions like this test whether you can recognize equivalent amounts across these formats.
18. A savings account earns interest at rates of $\frac{1}{16}$ annually for the first year, $6.3\%$ annually for the second year, and $0.0624$ annually for the third year. In which year is the interest rate highest?
    Answer: Second year, because $6.3\%$ converts to the highest decimal rate When comparing interest rates given in different formats, you need to convert them all to the same form—typically decimals—to determine which is highest. Let's convert each rate to decimal form. The first year rate is $\frac{1}{16}$. To convert this fraction: $\frac{1}{16} = 0.0625$. The second year rate is $6.3\%$. To convert a percentage to decimal form, divide by 100: $6.3\% = \frac{6.3}{100} = 0.063$. The third year rate is already given as $0.0624$. Now we can compare: 0.0625, 0.063, and 0.0624. Looking at the thousandths place helps us order these precisely: 0.063 > 0.0624 > 0.0625. Therefore, the second year has the highest interest rate. Answer choice A incorrectly claims that $\frac{1}{16}$ converts to the highest rate, but 0.0625 is actually the smallest of the three values. Answer choice C makes the error of assuming that 0.0624 is largest simply because it's already in decimal form—but being in decimal form doesn't make a number larger. Answer choice D incorrectly suggests the second and third years are tied, but 0.063 ≠ 0.0624. The correct answer is B because $6.3\%$ converts to 0.063, which is the highest decimal rate. Strategy tip: When comparing rates in mixed formats, always convert everything to decimals first. Remember that percentages become decimals by dividing by 100, and don't assume the format tells you anything about the size of the number.

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