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# Decimals as Fractions

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Have you ever tried to fix something? Using tools can be tricky and sometimes you will need to know about fractions and other times decimals and sometimes both! Look at what happened at the sixth grade social.

In the game room during the sixth grade social, the map of the world fell off of the wall. Mrs. Jennings was monitoring this group, and she was very glad that no one was hurt. During the event, she put the map to the side to be fixed later. On Monday, Aaron and Chris asked Mrs. Jennings if they could help Mr. Jones, the custodian, fix the map. Mrs. Jennings said "Certainly!" and gave the boys permission to stay in from recess. Mr. Jones came to the classroom with his tool box. The first thing he had the boys do was to measure the two holes that the map had fallen from. The holes both measured $1\frac{1}{4}$ " in diameter. While Mr. Jones went to get his power drill, he asked Chris and Aaron to select a peg that would best fit the two holes. Chris and Aaron have three different sized pegs to choose from.

Peg 1 is 1.27” in diameter.

Peg 2 is 1.23” in diameter.

Peg 3 is 1.21” in diameter.

Chris and Aaron are puzzled. They know that they need to select the peg that is the closest to the size of the hole. They just aren’t sure what to choose.

This is where you come in. In this Concept, you will learn all about converting decimals to fractions.

Once you know how to do this, you will be able to convert the peg sizes from decimals to fractions and selecting the correct one will be simple.

### Guidance

Decimals and fractions are related. They both represent a part of a whole. With a decimal, the part of a whole is written using a decimal point. With a fraction, the part of a whole is written using a fraction bar and has a numerator and a denominator. Because fractions and decimals are related, we can write decimals as fractions.

How do we write decimals as fractions?

We write a decimal as a fraction by using place value.

$.67$

Tens Ones Decimal Point Tenths Hundredths Thousandths Ten-Thousandths
. 6 7

If we read this fraction out loud, we say, “Sixty-seven hundredths.”

Converting this decimal to a fraction becomes easy because we have the numerator “67” and the denominator “hundredths.”

The fraction is described by reading the decimal.

Our answer is $\frac{67}{100}$ .

Our next step is to see if we can simplify this fraction. In this case, we can’t simplify the fraction so our answer remains the same.

Let’s look at another one.

$.5$

We can write this decimal in our place value chart.

Tens Ones Decimal Point Tenths Hundredths Thousandths Ten-Thousandths
. 5

We read this decimal as “five tenths.” The numerator is the five and the denominator is the place value of tenths.

Our answer is $\frac{5}{10}$ .

Our next step is to see if we can simplify the fraction. This fraction simplifies to one-half.

Our final answer is $\frac{1}{2}$ .

Now it is time for you to practice. Write the following decimals as fractions in simplest form.

#### Example A

$.8$

Solution: $\frac{8}{10} = \frac{4}{5}$

#### Example B

$.25$

Solution: $\frac{25}{100} = \frac{1}{4}$

#### Example C

$.75$

Solution: $\frac{75}{100} = \frac{3}{4}$

Now let's go back to the problem at the sixth grade social.

For Chris and Aaron to select the correct peg, they are going to have to convert the peg sizes into mixed numbers. Since the measurement of the holes is in mixed number form, if the peg size is in mixed number form we can easily compare.

$\text{Peg} \ 1 &= 1.27 = 1\frac{27}{100}\\\text{Peg} \ 2 &= 1.23 = 1\frac{23}{100}\\\text{Peg} \ 3 &= 1.21 = 1\frac{21}{100}$

Our holes measured $1 \frac{1}{4}''$ in diameter. Uh Oh, we can’t figure out which peg is the best choice because the fraction part of the peg sizes is written in hundredths. The fraction part of the hole size is written in fourths.

We can convert the $1\frac{1}{4}''$ to a denominator of 100.

$1\frac{1}{4}=1\frac{25}{100}$

By comparing the sizes, we can see easily now that pegs 1 and 2 are the closest in size to the hole. We need to use critical thinking to decide if one is better than the other. Since peg 1 is actually a little bit bigger than the hole, it would not fit.

Our answer is Peg 2. That one is the closest to the size of the holes, without being too big to fit in at all.

### Vocabulary

Decimal
a part of a whole written using place value and a decimal point.
Fraction
a part of a whole written with a fraction bar dividing the numerator and the denominator.

### Guided Practice

Here is one for you to try on your own.

Jessie has completed $.85$ of her homework. If she was going to express this number as a fraction what would the fraction be? Be sure to write your answer in simplest form.

First, notice that this decimal has two places, so we are working with hundredths. Therefore, the denominator of our fraction is going to be 100.

$\frac{85}{100}$

Now we can simplify this fraction.

$\frac{85}{100} = \frac{17}{20}$

### Practice

Directions: Write each decimal as a fraction. You do not need to simplify them.

1. .67

2. .33

3. .45

4. .27

5. .56

6. .7

7. .98

8. .32

9. .04

10. .07

11. .056

12. .897

13. .372

14. .652

15. .032