ISEE Lower Level Mathematics Achievement Quiz: Decimal Fraction Conversion

What this quiz covers

This quiz focuses on Decimal Fraction Conversion, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Lower Level Mathematics Achievement.

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.

Question 1

1. 0.07
2. 0.28 (correct answer)
3. 0.35
4. 0.7

Explanation: To convert (\frac{7}{25}) to a decimal, you can find an equivalent fraction with a denominator that is a power of 10, such as 100. To get from 25 to 100, you multiply by 4. Multiply the numerator by 4 as well: (7 \times 4 = 28). The equivalent fraction is (\frac{28}{100}), which is written as the decimal 0.28. Alternatively, you can divide 7 by 25.

Question 2

1. (\frac{1}{8}) foot (correct answer)
2. (\frac{1}{4}) foot
3. (\frac{1}{2}) foot
4. (\frac{5}{8}) foot

Explanation: First, convert 2.5 feet to a mixed number. The decimal 0.5 is equivalent to the fraction (\frac{1}{2}), so 2.5 is (2\frac{1}{2}) feet. To subtract (2\frac{3}{8}) from (2\frac{1}{2}), find a common denominator. (2\frac{1}{2}) is equivalent to (2\frac{4}{8}). Now subtract: (2\frac{4}{8} - 2\frac{3}{8} = \frac{1}{8}). The carpenter will have (\frac{1}{8}) foot of wood left over.

Question 3

1. (\frac{1}{12})
2. (\frac{3}{25}) (correct answer)
3. (\frac{12}{10})
4. (\frac{2}{15})

Explanation: The question asks for the fraction equivalent of the sales tax, which is $0.12. The cost of the pen,$1.50, is extra information. To convert 0.12 to a fraction, write it as (\frac{12}{100}). To simplify this fraction, divide both the numerator and denominator by their greatest common factor, 4. (12 \div 4 = 3) and (100 \div 4 = 25). The simplified fraction is (\frac{3}{25}).

Question 4

1. (\frac{3}{5}) m
2. (\frac{4}{5}) m
3. (\frac{11}{20}) m (correct answer)
4. (\frac{21}{20}) m

Explanation: First, convert the length of the first piece to a fraction. The decimal 0.8 is equal to (\frac{8}{10}), which simplifies to (\frac{4}{5}). The second piece is (\frac{1}{4}) meter shorter, so we need to subtract: (\frac{4}{5} - \frac{1}{4}). To do this, find a common denominator, which is 20. (\frac{4}{5} = \frac{16}{20}) and (\frac{1}{4} = \frac{5}{20}). Now subtract: (\frac{16}{20} - \frac{5}{20} = \frac{11}{20}). The length of the second piece is (\frac{11}{20}) meters.

Question 5

1. Aiden lives farthest from school.
2. Bella lives farthest from school. (correct answer)
3. Carlos lives closer than Aiden.
4. Aiden and Carlos live the same distance away.

Explanation: To compare the distances, convert all values to decimals. Aiden's distance is 0.6 miles. Bella's distance is (\frac{3}{4}), which is (3 \div 4 = 0.75) miles. Carlos's distance is (\frac{5}{8}), which is (5 \div 8 = 0.625) miles. Comparing the decimals: 0.6, 0.75, and 0.625. The greatest value is 0.75, so Bella lives farthest from school.

Question 6

1. (\frac{1}{4}) (correct answer)
2. (\frac{3}{10})
3. (\frac{1}{5})
4. (\frac{1}{2})

Explanation: To find the value halfway between two numbers, first express them in the same format. Convert (\frac{2}{5}) to a decimal: (2 \div 5 = 0.4). Now find the average of 0.1 and 0.4 by adding them and dividing by 2: ((0.1 + 0.4) \div 2 = 0.5 \div 2 = 0.25). Finally, convert the result, 0.25, back to a fraction. The decimal 0.25 is equivalent to (\frac{25}{100}), which simplifies to (\frac{1}{4}).

Question 7

1. $0.05$
2. $0.20$
3. $0.50$ (correct answer)
4. $0.25$

Explanation: This question tests the ability to convert between decimals and fractions, a key skill in ISEE Lower Level Mathematics Achievement. Converting between decimals and fractions involves understanding place value and equivalent values; for example, 0.5 is equivalent to 1/2 because it represents half. In the given scenario, Noah poured 1/2 cup of water, and we need to find the decimal equivalent of 1/2. The correct answer is 0.50 (or 0.5) because when we divide 1 by 2, we get 0.5, which represents half or 50 hundredths. A common distractor might be 0.25, which is 1/4 not 1/2, or 0.20 which is 1/5, showing confusion with common fraction values. To help students: Remember that 1/2 means one divided by two, which equals 0.5 or 0.50. Use visual aids like a circle cut in half to reinforce that 1/2 = 0.5 = 50%.

Question 8

1. $0.34$
2. $0.70$
3. $0.75$ (correct answer)
4. $0.80$

Explanation: This question tests the ability to convert between decimals and fractions, a key skill in ISEE Lower Level Mathematics Achievement. Converting between decimals and fractions involves understanding place value and equivalent values; for example, 0.5 is equivalent to 1/2 because it represents half. In the given scenario, Mina made 3/4 of her free throws, and we need to find the decimal equivalent of 3/4. The correct answer is 0.75 because when we divide 3 by 4, we get 0.75, or we can think of it as 3/4 = 75/100 = 0.75. A common distractor might be 0.34, which incorrectly combines the digits 3 and 4 without performing division, or 0.80 which represents 4/5, not 3/4. To help students: Practice dividing the numerator by the denominator using long division or a calculator to convert fractions to decimals. Remember that 3/4 means 3 divided by 4, which equals 0.75.

Question 9

1. $\dfrac{4}{10}$
2. $\dfrac{2}{5}$ (correct answer)
3. $\dfrac{1}{4}$
4. $\dfrac{40}{1}$

Explanation: This question tests the ability to convert between decimals and fractions, a key skill in ISEE Lower Level Mathematics Achievement. Converting between decimals and fractions involves understanding place value and equivalent values; for example, 0.5 is equivalent to 1/2 because it represents half. In the given scenario, Leila saved 0.40 of her money, and we need to convert 0.40 to a fraction. The correct answer is 2/5 because 0.40 means 40 hundredths, which can be written as 40/100, and when simplified by dividing both parts by 20, we get 2/5. A common distractor might be 4/10, which is equivalent but not in simplest form, or 1/4 which equals 0.25, not 0.40. To help students: Always simplify fractions to lowest terms by finding the greatest common factor. Practice checking your work by converting the fraction back to a decimal: 2/5 = 2 ÷ 5 = 0.40.

Question 10

1. $\dfrac{1}{20}$
2. $\dfrac{1}{2}$ (correct answer)
3. $\dfrac{2}{5}$
4. $\dfrac{3}{5}$

Explanation: This question tests the ability to convert between decimals and fractions, a key skill in ISEE Lower Level Mathematics Achievement. Converting between decimals and fractions involves understanding place value and equivalent values; for example, 0.5 is equivalent to 1/2 because it represents half. In the given scenario, Aisha used a coupon for $0.50 off, and we need to find the fraction that equals 0.50. The correct answer is 1/2 because 0.50 means 50 hundredths, which simplifies to 50/100 = 1/2 when we divide both numerator and denominator by 50. A common distractor might be 1/20, which represents 0.05, not 0.50, showing confusion with decimal place values. To help students: Practice converting decimals with zeros by first writing them as fractions over powers of 10, then simplifying. Remember that 0.50 = 0.5, and think of common benchmark fractions like 1/2, 1/4, and 3/4.

Question 11

1. $0.40$
2. $0.10$
3. $0.75$
4. $0.25$ (correct answer)

Explanation: This question tests the ability to convert between decimals and fractions, a key skill in ISEE Lower Level Mathematics Achievement. Converting between decimals and fractions involves understanding place value and equivalent values; for example, 0.5 is equivalent to 1/2 because it represents half. In the given scenario, Ethan hit 1/4 of his shots, and we need to find the decimal equivalent of 1/4. The correct answer is 0.25 because when we divide 1 by 4, we get 0.25, or we can think of it as 1/4 = 25/100 = 0.25. A common distractor might be 0.40, which is 2/5 not 1/4, or 0.10 which is 1/10, showing confusion with fraction values. To help students: Remember that 1/4 is one quarter, like a quarter dollar worth $0.25. Practice dividing 1 by 4 using long division or recognizing that 1/4 = 25/100 = 0.25.

Question 12

1. $\dfrac{3}{5}$
2. $\dfrac{6}{8}$
3. $\dfrac{3}{4}$ (correct answer)
4. $\dfrac{75}{1}$

Explanation: This question tests the ability to convert between decimals and fractions, a key skill in ISEE Lower Level Mathematics Achievement. Converting between decimals and fractions involves understanding place value and equivalent values; for example, 0.5 is equivalent to 1/2 because it represents half. In the given scenario, Sofia had $0.75 off using a coupon, and we need to find the fraction that equals 0.75. The correct answer is 3/4 because 0.75 means 75 hundredths, which can be written as 75/100, and when simplified by dividing both parts by 25, we get 3/4. A common distractor might be 3/5, which equals 0.60 not 0.75, or 6/8 which is equivalent to 3/4 but not in simplest form. To help students: Remember that 0.75 is three-quarters (like three quarter dollars), and always simplify fractions to their lowest terms. Practice recognizing that 0.75 = 75/100 = 3/4.

Question 13

1. $\dfrac{1}{4}$ (correct answer)
2. $\dfrac{1}{25}$
3. $\dfrac{25}{10}$
4. $\dfrac{2}{5}$

Explanation: This question tests the ability to convert between decimals and fractions, a key skill in ISEE Lower Level Mathematics Achievement. Converting between decimals and fractions involves understanding place value and equivalent values; for example, 0.5 is equivalent to 1/2 because it represents half. In the given scenario, Diego measured 0.25 cups of milk, and we need to convert 0.25 to a fraction. The correct answer is 1/4 because 0.25 means 25 hundredths, which can be written as 25/100, and when simplified by dividing both parts by 25, we get 1/4. A common distractor might be 1/25, which incorrectly uses the decimal digits without considering place value, or 2/5 which equals 0.40, not 0.25. To help students: Remember that 0.25 is a quarter (like a quarter dollar), and practice recognizing common decimal-fraction pairs. Use visual models like pie charts divided into fourths to reinforce that 1/4 = 0.25.

Question 14

1. (2\frac{7}{9})
2. (3\frac{1}{2})
3. (3\frac{3}{5})
4. (3\frac{11}{20}) (correct answer)

Explanation: To find the total growth, you need to add 1.8 and (1\frac{3}{4}). First, convert 1.8 to a mixed number. The decimal 0.8 is (\frac{8}{10}), which simplifies to (\frac{4}{5}). So, 1.8 is (1\frac{4}{5}). Now add (1\frac{4}{5}) and (1\frac{3}{4}). Find a common denominator, which is 20. (1\frac{4}{5} = 1\frac{16}{20}) and (1\frac{3}{4} = 1\frac{15}{20}). Add them: (1\frac{16}{20} + 1\frac{15}{20} = 2\frac{31}{20}). Since (\frac{31}{20}) is an improper fraction, convert it to a mixed number: (1\frac{11}{20}). Add this to the whole number 2: (2 + 1\frac{11}{20} = 3\frac{11}{20}).

Question 15

1. (\frac{15}{10})
2. (\frac{1}{5})
3. (\frac{3}{20}) (correct answer)
4. (\frac{3}{5})

Explanation: The decimal 0.15 represents fifteen-hundredths. As a fraction, this is written (\frac{15}{100}). To simplify, find the greatest common factor of 15 and 100, which is 5. Divide both the numerator and the denominator by 5: (15 \div 5 = 3) and (100 \div 5 = 20). The simplified fraction is (\frac{3}{20}).

Question 16

1. (\frac{1}{10}) (correct answer)
2. (\frac{1}{5})
3. (\frac{2}{5})
4. (\frac{4}{5})

Explanation: First, convert both lengths to fractions with a common denominator. The decimal 0.7 is equivalent to (\frac{7}{10}). The fraction (\frac{3}{5}) is equivalent to (\frac{6}{10}). To find the length of the remaining ribbon, subtract the cut piece from the original length: (\frac{7}{10} - \frac{6}{10} = \frac{1}{10}). The remaining ribbon is (\frac{1}{10}) of a meter long.

Question 17

1. 0.25 cups
2. 0.34 cups
3. 0.60 cups
4. 0.75 cups (correct answer)

Explanation: The question requires converting the fraction (\frac{3}{4}) to a decimal. You can find the decimal equivalent by dividing the numerator by the denominator: (3 \div 4 = 0.75). So, you should measure 0.75 cups of milk.

Question 18

1. $\dfrac{6}{10}$
2. $\dfrac{3}{5}$ (correct answer)
3. $\dfrac{1}{6}$
4. $\dfrac{60}{1}$

Explanation: This question tests the ability to convert between decimals and fractions, a key skill in ISEE Lower Level Mathematics Achievement. Converting between decimals and fractions involves understanding place value and equivalent values; for example, 0.5 is equivalent to 1/2 because it represents half. In the given scenario, Kai ran 0.60 of a mile in practice, and we need to convert 0.60 to a fraction. The correct answer is 3/5 because 0.60 means 60 hundredths, which can be written as 60/100, and when simplified by dividing both parts by 20, we get 3/5. A common distractor might be 6/10, which is equivalent but not in simplest form, or 1/6 which equals approximately 0.167, not 0.60. To help students: Remember to always simplify fractions by finding the greatest common factor of the numerator and denominator. Practice verifying your answer by converting back: 3/5 = 3 ÷ 5 = 0.60.

Question 19

1. (\frac{1}{3})
2. (\frac{2}{5})
3. (\frac{9}{20}) (correct answer)
4. (\frac{3}{5})

Explanation: To solve this, convert the decimals to fractions with a common denominator. 0.4 is equal to (\frac{4}{10}), which is (\frac{8}{20}). 0.5 is equal to (\frac{5}{10}), which is (\frac{10}{20}). The question asks for a fraction between (\frac{8}{20}) and (\frac{10}{20}). The fraction (\frac{9}{20}) is the only choice that falls within this range.

Question 20

1. (\frac{1}{2}, 0.6, \frac{3}{4}, 0.55)
2. (\frac{1}{2}, 0.55, 0.6, \frac{3}{4}) (correct answer)
3. (0.6, \frac{3}{4}, \frac{1}{2}, 0.55)
4. (0.55, \frac{1}{2}, 0.6, \frac{3}{4})

Explanation: To order the numbers, convert them all to the same format, such as decimals. (\frac{1}{2} = 0.5). (\frac{3}{4} = 0.75). The other numbers are already decimals: 0.6 and 0.55. Now, arrange these decimals in order from least to greatest: 0.5, 0.55, 0.6, 0.75. Finally, substitute the original forms back into the ordered list: (\frac{1}{2}), 0.55, 0.6, (\frac{3}{4}).