# Comparison of Ratios in Decimal Form

## Rewrite ratios as decimals.

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Comparison of Ratios in Decimal Form

Remember Casey and the milk comparison in the Ratios in Simplest Form Concept? Well, look at what she is up to now.

Casey decided to hold a survey about the milk choices of customers at the supermarket. She discovers that many people purchase regular milk and half as many purchase organic milk. Casey surveyed 50 people.

Here is what she found.

35 out of 50 purchased regular milk.

15 out of 50 purchased organic milk.

If Casey wanted to think about these ratios as decimals, could she do it? What would the decimals be for each choice?

This Concept will teach you how to do these conversions.

### Guidance

Previously we worked on writing ratios in fraction form and simplifying them. What about decimal form? Fractions and decimals are related, in fact a fraction can be written as a decimal and a decimal can be written as a fraction.

Is it possible to write a ratio as a decimal too?

Yes! Because a ratio can be written as a fraction, it can also be written as a decimal. To do this, you will need to remember how to convert fractions to decimals.

Now we can apply this information to our work with ratios.

Convert 2:4 into a decimal.

First, write it as a ratio in fraction form.

\begin{align*}2:4 = \frac{2}{4}\end{align*}

Next, simplify the fraction if possible.

\begin{align*}\frac{2}{4} = \frac{1}{2}\end{align*}

Finally, convert the fraction to a decimal.

\begin{align*} \overset{\quad .5}{2\overline{)1.0 \;}}\end{align*}

Our answer is .5.

Practice by converting each ratio to decimal form.

4 to 5

Solution: .80

#### Example B

\begin{align*}\frac{5}{20}\end{align*}

Solution: .25

#### Example C

6 to 10

Solution: .60

Now let's go and help Casey convert her ratios into decimal form. Here is the original problem once again.

Remember Casey and the milk comparison? Well, look at what she is up to now.

Casey decided to hold a survey about the milk choices of customers at the supermarket. She discovers that many people purchase regular milk and half as many purchase organic milk. Casey surveyed 50 people.

Here is what she found.

35 out of 50 purchased regular milk.

15 out of 50 purchased organic milk.

If Casey wanted to think about these ratios as decimals, could she do it? What would the decimals be for each choice?

First, we can write a ratio in fraction form. We can use convert the ratios.

\begin{align*} \frac{35}{50} = \frac{70}{100}\end{align*}

\begin{align*} \frac{15}{50} = \frac{30}{100}\end{align*}

The first decimal is .70.

The second decimal is .30.

### Guided Practice

Here is one for you to try on your own.

Write 2 out of 25 as a decimal.

Answer

To write this ratio as a decimal, we can use a denominator of 100 and create equal fractions.

\begin{align*} \frac{2}{25} = \frac{?}{100}\end{align*}

Next, we figure out the unknown quantity.

25 times 4 = 100

2 times 4 = 8

\begin{align*} \frac{8}{100}\end{align*}

Our answer is .08.

### Explore More

Directions: Convert the following ratios into decimals.

1. 3 to 4

2. 2 to 4

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

4. 25 to 100

5. 16 to 32

6. 4 out of 5

7. 6 out of 20

8. \begin{align*} \frac{1}{4}\end{align*}

9. 5 to 6

10. 1:2

11. 4:10

12. 10:50

13. 75 to 100

14. 1 to 3

15. 6 to 8

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### Vocabulary Language: English

TermDefinition
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).
Equivalent Equivalent means equal in value or meaning.
Greatest Common Factor The greatest common factor of two numbers is the greatest number that both of the original numbers can be divided by evenly.
Simplify To simplify means to rewrite an expression to make it as "simple" as possible. You can simplify by removing parentheses, combining like terms, or reducing fractions.

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