Decimal-Fraction Conversion - ISEE Lower Level Mathematics Achievement

A scientist measured a sample to be 0.045 kilograms. What is this measurement as a fraction of a kilogram in simplest form?
Answer: $\frac{9}{200}$ The decimal 0.045 has its last digit in the thousandths place, so it can be written as the fraction $\frac{45}{1000}$ . To simplify this fraction, find the greatest common factor of 45 and 1000, which is 5. Divide both the numerator and denominator by 5: $45 \div 5 = 9$ and $1000 \div 5 = 200$ . The simplified fraction is $\frac{9}{200}$ .
A baker uses 0.375 of a bag of flour for a batch of cookies. What fraction of the bag of flour did the baker use?
Answer: $\frac{3}{8}$ To convert the decimal 0.375 to a fraction, write it based on its place value. The last digit is in the thousandths place, so we have $\frac{375}{1000}$ . To simplify, find the greatest common factor. Both numbers are divisible by 25, and then by 5 (or by 125). $375 \div 125 = 3$ and $1000 \div 125 = 8$ . The simplified fraction is $\frac{3}{8}$ .
Which of the following lists of numbers is in order from least to greatest?
Answer: $\frac{1}{2}, 0.55, 0.6, \frac{3}{4}$ 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, $\frac{3}{4}$ .
Aisha used a coupon for $0.50 off. Which fraction equals $0.50?
Answer: $\dfrac{1}{2}$ 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.
Priya split $0.20$ of supplies equally. What fraction equals $0.20$ ? Give your answer in simplest form.
Answer: $\dfrac{1}{5}$ 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, Priya split 0.20 of supplies equally, and we need to find the fraction that equals 0.20. The correct answer is 1/5 because 0.20 means 20 hundredths, which can be written as 20/100, and when simplified by dividing both parts by 20, we get 1/5. A common distractor might be 2/10, which is equivalent but not in simplest form, or 1/20 which equals 0.05, not 0.20. To help students: Always reduce fractions to simplest form, and remember that 0.20 = 0.2 = 2/10 = 1/5. Practice recognizing that moving the decimal two places gives you the fraction over 100.
The number 0.36 can be written as an equivalent fraction $\frac{N}{25}$ . What is the value of N?
Answer: 9 First, write 0.36 as a fraction based on its place value: $\frac{36}{100}$ . To find the equivalent fraction with a denominator of 25, you must simplify $\frac{36}{100}$ . Divide both the numerator and the denominator by their greatest common factor, which is 4. $36 \div 4 = 9$ and $100 \div 4 = 25$ . So, the equivalent fraction is $\frac{9}{25}$ . Therefore, the value of N is 9.
Which fraction has a value that is greater than 0.4 but less than 0.5?
Answer: $\frac{9}{20}$ 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.
Mina made $\dfrac{3}{4}$ of her free throws. What decimal is $\dfrac{3}{4}$ ?
Answer: $0.75$ 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.
A length of rope is cut into two pieces. The first piece is 0.8 meters long. The second piece is $\frac{1}{4}$ meter shorter than the first piece. What is the length of the second piece, expressed as a fraction of a meter?
Answer: $\frac{11}{20}$ m 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.
Which of the following decimal values is equal to the fraction $\frac{5}{8}$ ?
Answer: 0.625 To convert a fraction to a decimal, divide the numerator by the denominator. So, divide 5 by 8. Since 5 is smaller than 8, you'll be working with decimals. $5 \div 8 = 0.625$ .
What is the sum of 0.8 and $\frac{1}{10}$ , expressed as a fraction in simplest form?
Answer: $\frac{9}{10}$ To add a decimal and a fraction, first convert the decimal to a fraction. The decimal 0.8 is equivalent to $\frac{8}{10}$ . Now, add the two fractions: $\frac{8}{10} + \frac{1}{10} = \frac{9}{10}$ . This fraction is already in its simplest form.
Diego measured $0.25$ cups of milk. Convert $0.25$ to a fraction.
Answer: $\dfrac{1}{4}$ 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.
A carpenter has a piece of wood that is 2.5 feet long. He uses a piece that is $2\frac{3}{8}$ feet long for a project. How much wood will he have left over, expressed as a fraction of a foot?
Answer: $\frac{1}{8}$ foot 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.
A video game takes 3.4 hours to complete. Which mixed number is equivalent to 3.4?
Answer: $3\frac{2}{5}$ The number 3.4 is composed of a whole number part (3) and a decimal part (0.4). The decimal 0.4 means four-tenths, which can be written as the fraction $\frac{4}{10}$ . This fraction can be simplified by dividing the numerator and denominator by 2, which gives $\frac{2}{5}$ . Combining the whole number and the simplified fraction gives the mixed number $3\frac{2}{5}$ .
A new pen costs $1.50. The sales tax on the pen is $0.12. What fraction of a dollar is the sales tax, in simplest form?
Answer: $\frac{3}{25}$ 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 $\frac{3}{25}$ .
Leila saved $0.40$ of her money. Convert $0.40$ to a fraction. Give your answer in simplest form.
Answer: $\dfrac{2}{5}$ 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.
A recipe requires $\frac{3}{4}$ cup of milk. If you only have a measuring cup with decimal markings, how much milk should you measure?
Answer: 0.75 cups 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.
Find the value that is halfway between 0.1 and $\frac{2}{5}$ . Express your answer as a fraction.
Answer: $\frac{1}{4}$ 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 $\frac{1}{4}$ .
Sofia had $0.75$ off using a coupon. What fraction equals $0.75$ ? Give your answer in simplest form.
Answer: $\dfrac{3}{4}$ 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.
In a class survey, 0.15 of the students chose red as their favorite color. What fraction of the students, in simplest form, chose red?
Answer: $\frac{3}{20}$ 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 $\frac{3}{20}$ .

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