5th Grade Math Help: Making Decimals Into Fractions or Whole Numbers

Changing Decimals to Fractions

All whole numbers and many decimals are rational numbers, which means that they can be written as fractions. In order to do this, you need to understand place values, so let's do a quick review.

Place Values

In a decimal, the whole number part of the amount is shown on the left side of the decimal point. The first number to the left of the decimal point is in the ones place, the second number is in the tens place and the third number is in the hundreds place. The fractional part of the amount is shown on the right side of the decimal. The first number to the right of the decimal point is in the tenths place, the second number is in the hundredths place and the third number is in the thousandths place.

Decimals

Let's start with simple decimals, like 0.4. Since this decimal only has a digit in the tenths place, we can write it as a fraction by putting four over ten, like this: 4/10. Likewise, 0.1 = 1/10, 0.6 = 6/10 and 0.9 = 9/10. For decimals with a digit in the hundredths place, you'll need to drop the decimal point and put the numbers over 100. For instance, 0.42 = 42/100, 0.13 = 13/100 and 0.97 = 97/100. If there's a digit in the thousandths place, you drop the decimal point and put the numbers over 1,000. Practice by writing these decimals as fractions:

1. 0.34

2. 0.2

3. 0.988

Solutions

1. 0.34 = 34/100

2. 0.2 = 2/10

3. 0.988 = 988/1000

Whole Numbers

Some decimals, like 5.0 and 40.0, are already equal to whole numbers. To change a whole-number decimal to a fraction, put the number as the numerator, and then put one as the denominator. For example, 7.0 = 7/1, 19.0 = 19/1 and 84.0 = 84/1. Complete these practice problems by writing each decimal as a fraction:

1. 9.0

2. 37.0

3. 100.0

Solutions

1. 9.0 = 9/1

2. 37.0 = 37/1

3. 100.0 = 100/1

Mixed Numbers

To write a decimal that's larger than one, like 5.25, as a fraction, you'll need to use mixed numbers. A mixed number is a number that includes a whole number and a fraction, like 3 1/4. The whole number in the decimal becomes the whole number part of the mixed number. For the fraction part of the mixed number, write the digits to the right of the decimal point as a fraction, and then simplify it if necessary. For 5.25, you would change it to 5 25/100, and then simplify to 5 1/4. Practice by changing these decimals to mixed numbers:

1. 1.5

2. 8.75

3. 20.8

Solutions

1. 1.5 = 1 5/10 = 1 1/2

2. 8.75 = 8 75/100 = 8 3/4

3. 20.8 = 20 8/10 = 20 4/5