GRE Math : Decimals with Fractions

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Example Questions

Example Question #1 : Decimals With Fractions

Convert $\frac{23}{5}$ to an equivalent decimal number.

Possible Answers:

4.5

4.05

5.5

4.6

4.06

Correct answer:

4.6

Explanation:

To convert this fraction to a decimal number, divide the numerator by the denominator. Since this fraction has a larger numerator than denominator, the fraction is classified as an improper fraction. This means that the fraction represents a value greater than one whole. Thus, the solution must be greater than one.

$\frac{23}{5}=23\div5= 4.6$

Note that fits into evenly times, and has a remainder for of $\frac{3}{5}=\frac{6}{10}=0.6$

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Example Question #1 : How To Find Decimal Fractions

Find the decimal equivalent of $\frac{34}{200}$ .

Possible Answers:

0.17

0.34

1.7

0.034

0.017

Correct answer:

0.17

Explanation:

Fractions and decimals both represent part of a whole. To solve this problem you may divide by 200 , or you can reduce the fraction by dividing the numerator and denominator by the common factor of This will equal a fraction of hundredths, which can be written as the decimal number "zero and hundredths."

$\frac{34}{200}=\frac{34\div 2}{200\div 2}=\frac{17}{100}=0.17$

Note: both $34\div200$ and $17\div100$ equal 0.17

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Example Question #1 : Decimals With Fractions

Find the fractional equivalent for 0.707 .

Possible Answers:

$\frac{77}{100}$

$\frac{70}{100}$

$\frac{770}{1,000}$

$\frac{707}{1,000}$

$\frac{70}{1,000}$

Correct answer:

$\frac{707}{1,000}$

Explanation:

Decimal numbers and fractions both represent part of a whole. This decimal number has a value of in the tenths and thousandths place values. Since the decimal number reaches the thousandths place, the correct answer is 707 over 1,000 --which represents 707 thousandths.

$0.707=\frac{707}{1,000}$

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Example Question #1 : Decimals With Fractions

Convert 1.08 to a mixed number fraction. Then simplify your answer.

Possible Answers:

$\frac{8}{10}$

$1\frac{1}{2}$

$1\frac{16}{100}$

$1\frac{2}{25}$

$1\frac{8}{10}$

Correct answer:

$1\frac{2}{25}$

Explanation:

Both decimals and fractions represent part of a whole. To convert this decimal number to a mixed number fraction, use the following steps:

$1.08=1\frac{8}{100}$

(because the decimal number has a in the ones place value and an in the hundredths place value).

Then simplify $\frac{8}{100}$ .

$\frac{8}{100}=\frac{4}{50}=\frac{2}{25}$

Thus, the correct answer is $1\frac{2}{25}$

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Example Question #3 : How To Find Decimal Fractions

Convert 0.98 to a fraction. Then simplify.

Possible Answers:

$\frac{98}{100}$

$\frac{9}{10}$

$\frac{24}{25}$

$\frac{49}{50}$

$\frac{98}{10}$

Correct answer:

$\frac{49}{50}$

Explanation:

Both decimals and fractions represent part of a whole. Since this decimal number has a value of in the tenths place and a value of in the hundredths place, it can be re-written as:

$\frac{98}{100}$ .

Then, simplify the fraction by dividing both the numerator and denominator by a divisor of

Thus, the solution is:

$0.98=\frac{98}{100}=\frac{98\div 2}{100\div 2}=\frac{49}{50}$

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Example Question #3 : Decimals With Fractions

Find the fractional equivalent to 8.045 .

Possible Answers:

$\frac{845}{100}$

$\frac{1,609}{200}$

$8\frac{45}{10}$

$\frac{1,600}{200}$

$8\frac{45}{100}$

Correct answer:

$\frac{1,609}{200}$

Explanation:

This problem requires several conversions. First, convert 8.045 into a mixed number fraction. This means, the new fraction will have a whole number of and a fraction that represents thousandths. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number, and then add that product to the numerator.

Thus, the solution is:

$8.045=8\frac{45}{1,000}=8\frac{45\div 5}{1,000\div 5}=8\frac{9}{200}=\frac{(8\times 200)+9}{200}=\frac{1,609}{200}$

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Example Question #4 : How To Find Decimal Fractions

Convert 6.70 to an improper fraction.

Possible Answers:

$\frac{67}{10}$

$\frac{67}{100}$

$\frac{76}{10}$

$\frac{6}{10}$

$\frac{70}{6}$

Correct answer:

$\frac{67}{10}$

Explanation:

This problem requires two conversions. First convert 6.7 to a mixed number fraction. This must equal a whole number of and a fraction that represents a value of tenths. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number, and then add that product to the numerator.

Thus, the solution is:
$6.70=6\frac{7}{10}=\frac{(6\times 10)+7}{10}=\frac{67}{10}$

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Example Question #2 : Decimals With Fractions

Find the fractional equivalent to 2.25 . Then reduce the fraction if possible.

Possible Answers:

$2\frac{3}{4}$

$\frac{25}{100}$

$2\frac{25}{10}$

$2\frac{4}{10}$

$2\frac{1}{4}$

Correct answer:

$2\frac{1}{4}$

Explanation:

To solve this problem, make a mixed number fraction with a whole number of and a fraction that represents hundredths. Then simplify the fraction portion of the mixed number by dividing the numerator and denominator by their largest common divisor.

$2.25=2\frac{25}{100}=2\frac{25\div 25}{100\div 25}=2\frac{1}{4}$

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Example Question #1 : How To Find Decimal Fractions

Find the fractional equivalent to 3.504 . Then simplify.

Possible Answers:

$3\frac{120}{250}$

$3\frac{63}{125}$

$3\frac{54}{1,000}$

$3\frac{4}{5}$

$3\frac{54}{100}$

Correct answer:

$3\frac{63}{125}$

Explanation:

This problem requires you to first convert the decimal number to a mixed number fraction that has a whole number of and a fraction that represents 504 thousandths. Then reduce the numerator and denominator by common divisors until you can no longer simplify the fraction.

$3.504=3\frac{504}{1,000}=3\frac{504\div 4}{1,000\div 4}=3\frac{126}{250}=3\frac{126\div 2}{250\div 2}=3\frac{63}{125}$

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Example Question #4 : Decimals With Fractions

Convert 0.0646 to a fraction. Then simplify.

Possible Answers:

$\frac{323}{5,000}$

$\frac{323}{10,000}$

$\frac{323}{500}$

$\frac{646}{1,000}$

$\frac{46}{100}$

Correct answer:

$\frac{323}{5,000}$

Explanation:

Both fractions and decimals represent part of a whole. The value of this decimal number reaches the ten-thousandths place value. Thus, the fraction must represent 646 ten-thousandths. Then reduce the numerator and denominator by the common divisor of .

$0.0646=\frac{646}{10,000}=\frac{646\div 2}{10,000\div 2}=\frac{323}{5,000}$

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GRE Math : Decimals with Fractions

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : Decimals With Fractions

Example Question #1 : How To Find Decimal Fractions

Example Question #1 : Decimals With Fractions

Example Question #1 : Decimals With Fractions

Example Question #3 : How To Find Decimal Fractions

Example Question #3 : Decimals With Fractions

Example Question #4 : How To Find Decimal Fractions

Example Question #2 : Decimals With Fractions

Example Question #1 : How To Find Decimal Fractions

Example Question #4 : Decimals With Fractions

All GRE Math Resources

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