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# Decimals as Fractions

## Fractions with 10, 100 or 1000 as denominators

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Decimals as Fractions

Have you ever had a friend who loved math so much that they included it into all of their conversations? Well, look at Jessie and Fiona.

Jessie loves math. She and Fiona were discussing the bake sale, and Jessie had to put in some math.

"I think I will eat .75 of a whole cake," She said grinning.

Fiona looked wryly at her friend.

Do you know what this amount of cake is as a fraction?

This Concept is about writing decimals as fractions. You will be able to figure this out by the end of the Concept.

### Guidance

Previously we worked on writing fractions as decimals, it will be good to know how to go back the other way and write decimals as fractions.

Consider again the decimal 0.1. We already know that we can say that this number is “one-tenth.” It’s very easy to rewrite decimals as fractions because decimals are already expressed as fractions with a denominator that is a factor of ten.

0.1=110,0.01=1100\begin{align*}0.1 = \frac{1}{10}, 0.01 = \frac{1}{100}\end{align*}

We can also say that 0.86=86100\begin{align*}0.86 = \frac{86}{100}\end{align*}.

To convert decimals to fractions, we write the number to the right of the decimal place over a denominator equivalent to the last place value of the decimal number. So, if we have 0.877, we would write 8771000\begin{align*}\frac{877}{1000}\end{align*}.

If we have simply 0.6, we can write 610\begin{align*}\frac{6}{10}\end{align*}, or in simplest terms, 35\begin{align*}\frac{3}{5}\end{align*}. Always make sure to put your fraction in simplest terms.

Convert 0.35 to a fraction.

Start by saying the decimal to yourself out loud. To say 0.35 out loud, we can say “35 hundredths,” so we can go ahead and write the fraction down.

35100\begin{align*}\frac{35}{100}\end{align*}

That’s a big fraction. We want to make our lives a little bit easier, so we will reduce the fraction to simplest terms. This fraction expressed in simplest terms is 720\begin{align*}\frac{7}{20}\end{align*}.

Our final answer is 720\begin{align*}\frac{7}{20}\end{align*}.

Here is another one.

Convert 2.4 to a mixed number.

Just as we leave aside the whole number when converting mixed numbers to decimals, we will leave aside the numbers to the left of the decimal point when converting decimals to fractions. So, in this case, we just have to find out what 0.4 is expressed as a fraction.

Let’s write it directly as the fraction “four tenths” or 410\begin{align*}\frac{4}{10}\end{align*}. Can we simplify it? You bet. 410=25\begin{align*}\frac{4}{10}=\frac{2}{5}\end{align*}.

2.4 expressed as a mixed number =225\begin{align*}= 2 \frac{2}{5}\end{align*}.

Now it's your turn to try a few. Write each decimal as a fraction or mixed number.

#### Example A

0.5\begin{align*}0.5\end{align*}

Solution: 510\begin{align*}\frac{5}{10}\end{align*}

#### Example B

0.67\begin{align*}0.67\end{align*}

Solution: 67100\begin{align*}\frac{67}{100}\end{align*}

#### Example C

3.21\begin{align*}3.21\end{align*}

Solution: 321100\begin{align*}3 \frac{21}{100}\end{align*}

Here is the original problem once again.

Jessie loves math. She and Fiona were discussing the bake sale, and Jessie had to put in some math.

"I think I will eat .75 of a whole cake," She said grinning.

Fiona looked wryly at her friend.

Do you know what this amount of cake is as a fraction?

To figure this out, we can change the decimal to a fraction with a base ten denominator.

This decimal has two decimal places represented. That means hundredths.

Here is the decimal as a fraction with a base ten denominator.

.75=75100\begin{align*}.75 = \frac{75}{100}\end{align*}

Now we can simplify the fraction.

75100=34\begin{align*}\frac{75}{100} = \frac{3}{4}\end{align*}

This is our answer.

### Vocabulary

Fraction
a part of a whole written using a numerator and a denominator and a fraction bar
Decimal
a part of a whole written using a decimal point and place value
Mixed Number
a number written with a whole number and a fraction.

### Guided Practice

Here is one for you to try on your own.

Write the following decimal as a fraction or mixed number in simplest form.

5.25\begin{align*}5.25\end{align*}

Answer

First, you can see that this decimal has wholes and parts, so it will become a mixed number.

5\begin{align*}5\end{align*} is the whole.

0.25\begin{align*}0.25\end{align*} is the parts.

.25=25100=14\begin{align*}.25 = \frac{25}{100} = \frac{1}{4}\end{align*}

Our answer is 514\begin{align*}5 \frac{1}{4}\end{align*}.

### Practice

Directions: Write each decimal as a fraction in simplest form.

1. .3

2. .4

3. .2

4. .53

5. .55

6. .08

7. .25

8. .23

9. .876

10. .512

11. 74.34

12. 3.88

13. 5.6

14. 12.8

15. 23.06

16. .987

### Vocabulary Language: English

Decimal

Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).
fraction

fraction

A fraction is a part of a whole. A fraction is written mathematically as one value on top of another, separated by a fraction bar. It is also called a rational number.
Mixed Number

Mixed Number

A mixed number is a number made up of a whole number and a fraction, such as $4\frac{3}{5}$.

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