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# Fractions as Decimals

## Dividing the denominator into the numerator

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Fractions as Decimals

Have you ever eaten a portion of a pie and wondered how much you actually ate? Well, look at what Daniel ate.

Daniel loves peach pie. At the bake sale, he bought an entire peach pie. Then he went home, poured himself a glass of milk and ate 38\begin{align*}\frac{3}{8}\end{align*} of the pie.

What is this fraction as a decimal?

Do you know how to figure this out?

This Concept will teach you how to write fractions and mixed numbers as terminating decimals. You will know how to write Daniel's part of the pie by the end of the Concept.

### Guidance

Previously we worked on fractions and their corresponding operations, now it’s time to discover how they relate to decimals.

Fractions and decimals are related because they are both ways of describing numbers that are not wholes. In essence, a fraction is simply another way of describing what a decimal describes. They both represents parts of a whole and both can show the same part in a different way. The fraction shows us the part using the fraction bar comparing part to whole and the decimal shows us the part using place value. To start off, we’ll see how fractions can be converted into decimals and how decimals can be converted into fractions.

How do we convert fractions to decimals and decimals to fractions?

First, remember that fractions and decimals are different ways of writing the same thing. Both show us how to represent a part of a whole. Think about how we talk about fractions and decimals because this will become useful as we convert them.

Say this value out loud 0.1. You can say “point one” or you can say “one tenth.” Does the second version sound a little bit familiar? It sounds like the fraction 110\begin{align*}\frac{1}{10}\end{align*}. It turns out that 0.1=110\begin{align*}0.1 = \frac{1}{10}\end{align*}.

Yes. The quantities are the same.

How do we convert fractions into decimals?

We can easily convert fractions into decimals. You’ve probably noticed by now that a fraction is really a short way of writing a division expression. Writing 34\begin{align*}\frac{3}{4}\end{align*} is really like writing 3÷4\begin{align*}3 \div 4\end{align*}. The way that we find out how to write 34\begin{align*}\frac{3}{4}\end{align*} as a decimal is to go ahead and solve the division problem. Since 4 doesn’t go into 3, we have to expand the number over the decimal point.

4)3.0¯¯¯¯¯¯

How many times does 4 go into 3.0? Four goes into 3.0 .7 times.

4)3.0¯¯¯¯¯¯    .72.8  .2

Be sure when you are writing your quotient above the dividend to keep the original place of the decimal point. Since 4 does not divide evenly into 3.0 and we have a remainder of .2, we can go further to the other side of the decimal point by adding a 0 next to the remainder of .2.

4)3.00¯¯¯¯¯¯¯¯    .75  2.8   .20   .20      0

4 goes evenly into .20 five times, so we have our final answer.

34=0.75\begin{align*}\frac{3}{4} = 0.75\end{align*}

Convert 14\begin{align*}\frac{1}{4}\end{align*} to a decimal.

We start this by changing it into a division problem. We will be dividing 1 by 4. You already know that 1 can’t be divided by four, so you will need to use a decimal point and add zeros as needed.

4)1.00¯¯¯¯¯¯¯¯    .258  20  20 0

How do we convert mixed numbers to decimals?

When you are working with mixed numbers like 134\begin{align*}1 \frac{3}{4}\end{align*} for example, it is easiest to simply set the whole number to the side and solve the division problem with the fraction. When you have completed the division problem with the fraction, make sure that you put the whole number back on the left side of the decimal point.

134=1.75\begin{align*}1 \frac{3}{4} = 1.75\end{align*}

Convert 312\begin{align*}3 \frac{1}{2}\end{align*} to a decimal.

First, set aside the 3. We will come back to that later.

Next, we divide 1 by 2. Use a decimal point and zeros as needed.

2)1.0¯¯¯¯¯¯    .5 10 0

Now we add in the 3.

Now it's your turn. Convert each fraction or mixed number to a decimal.

#### Example A

15\begin{align*}\frac{1}{5}\end{align*}

Solution:.2\begin{align*}.2\end{align*}

#### Example B

36\begin{align*}\frac{3}{6}\end{align*}

Solution:.5\begin{align*}.5\end{align*}

#### Example C

445\begin{align*}4 \frac{4}{5}\end{align*}

Solution:4.8\begin{align*}4.8\end{align*}

Here is the original problem once again.

Daniel loves peach pie. At the bake sale, he bought an entire peach pie. Then he went home, poured himself a glass of milk and ate 38\begin{align*}\frac{3}{8}\end{align*} of the pie.

What is this fraction as a decimal?

Do you know how to figure this out?

To figure this out, we are going to divide the numerator by the denominator.

3÷8=?\begin{align*}3 \div 8 = ?\end{align*}

To do this, we will need to add decimals and divide.

.375\begin{align*}.375\end{align*}

### 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.
Terminating Decimal
a decimal with an ending.

### Guided Practice

Here is one for you to try on your own.

Convert the following mixed number to a decimal.

435\begin{align*}4 \frac{3}{5}\end{align*}

First, convert the mixed number to an improper fraction.

435=235\begin{align*}4 \frac{3}{5} = \frac{23}{5}\end{align*}

Now, we divide the numerator by the denominator.

23÷5=4.6\begin{align*}23 \div 5 = 4.6\end{align*}

### Video Review

http://www.youtube.com/watch?v=P0IB7LfeaU4 - This is a James Sousa video on writing fractions as terminating decimals.

### Practice

Directions: Write each fraction or mixed number as a decimal.

1. 35\begin{align*}\frac{3}{5}\end{align*}

2. 12\begin{align*}\frac{1}{2}\end{align*}

3. 45\begin{align*}\frac{4}{5}\end{align*}

4. \begin{align*}\frac{3}{4}\end{align*}

5. \begin{align*}\frac{3}{8}\end{align*}

6. \begin{align*}\frac{7}{8}\end{align*}

7. \begin{align*}2 \frac{1}{4}\end{align*}

8. \begin{align*}5 \frac{2}{5}\end{align*}

9. \begin{align*}6 \frac{4}{8}\end{align*}

10. \begin{align*}11 \frac{5}{8}\end{align*}

11. \begin{align*}10 \frac{1}{2}\end{align*}

12. \begin{align*}18 \frac{3}{4}\end{align*}

13. \begin{align*}12 \frac{4}{5}\end{align*}

14. \begin{align*}19 \frac{3}{4}\end{align*}

15. \begin{align*}22 \frac{1}{4}\end{align*}

### 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.
Irrational Number

Irrational Number

An irrational number is a number that can not be expressed exactly as the quotient of two integers.
Mixed Number

Mixed Number

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

Place Value

The value of given a digit in a multi-digit number that is indicated by the place or position of the digit.
Terminating Decimal

Terminating Decimal

A terminating decimal is a decimal number that ends. The decimal number 0.25 is an example of a terminating decimal.