# GRE Math : How to find decimal fractions

## Example Questions

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### Example Question #1 : How To Find Decimal Fractions

Convert  to an equivalent decimal number.

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.

Note that  fits into  evenly  times, and has a remainder for of

### Example Question #2 : Decimals With Fractions

Find the decimal equivalent of

Explanation:

Fractions and decimals both represent part of a whole. To solve this problem you may divide  by , 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."

Note: both  and  equal

### Example Question #3 : Decimals With Fractions

Find the fractional equivalent for .

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  over --which represents  thousandths.

### Example Question #4 : Decimals With Fractions

Explanation:

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

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

Then simplify .

### Example Question #5 : Decimals With Fractions

Convert  to a fraction. Then simplify.

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:

.

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

Thus, the solution is:

### Example Question #2 : How To Find Decimal Fractions

Find the fractional equivalent to

Explanation:

This problem requires several conversions. First, convert  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:

### Example Question #7 : Decimals With Fractions

Convert  to an improper fraction.

Explanation:

This problem requires two conversions. First convert  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:

### Example Question #8 : Decimals With Fractions

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

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.

### Example Question #42 : Decimals

Find the fractional equivalent to . Then simplify.

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  thousandths. Then reduce the numerator and denominator by common divisors until you can no longer simplify the fraction.

### Example Question #10 : Decimals With Fractions

Convert  to a fraction. Then simplify.