 # Convert from decimals to fractions

Lesson
Knowing the place value of decimals really helps us when we're changing decimals to fractions. The names of the decimal place values tell us about the denominators of their corresponding fraction. A decimal that finishes in the tenths column will have a denominator of $10$10 when we write it as a fraction, a decimal that finishes in the hundredths column will have a denominator of $100$100 when we write it as a fraction and so on. Once you work out the fraction like this, remember to check if it can be simplified. Let me show you what I mean with some diagrams. The decimal I have written in the place value table is $0.17$0.17. You can see that the last number I've written is in the hundredths column, so the denominator (bottom number) of our fraction is $100$100. As a fraction, we would write this as $\frac{17}{100}$17100.

#### Examples

##### question 1

Evaluate: Express $0.4$0.4 as a fraction in its simplest form.

Think: This decimal finishes in the tenths column

Do: $\frac{4}{10}$410= $\frac{2}{5}$25

We can convert any decimal in the same way!

##### Question 2

Evaluate: Express $0.08$0.08 as a fraction in its simplest form.

Think: This decimal finishes in the hundredths column

Do: $\frac{8}{100}$8100= $\frac{2}{25}$225

##### question 3

Evaluate: Express $0.155$0.155 as a fraction in its simplest form.

Think: This decimal finishes in the thousandths column

Do: $\frac{155}{1000}$1551000 = $\frac{31}{200}$31200

## Mixed numbers

Just keep on using the same pattern when you are writing numbers with decimals as a mixed number.

Remember- the number to the left of the decimal point does not have to change.

#### Examples

##### question 4

Evaluate: Convert $5.12$5.12 to a mixed number

Think: The $5$5 is a whole number and the decimal finishes in the hundredths column

Do: $5\frac{12}{100}=5\frac{3}{25}$512100=5325

##### Question 5

Evaluate: Convert $17.1$17.1 to a mixed number

ThinkThe $17$17 is a whole number and the decimal finishes in the tenths column

Do: $17\frac{1}{10}$17110

## Expressing decimals as the sum of integers and fractions

This may sound a bit fancy but really it just means "write each number according to its place value and then write all the numbers as an addition." You have already done this with whole numbers, so let's look at some examples with decimals. These questions normally say we don't need to simplify the fractions.

#### Examples

##### question 6

Evaluate: Express $18.97$18.97 as the sum of integers and fractions. Fractions do not need to be simplified.

Think: Remember the place value of each number.

Do: $10+8+\frac{9}{10}+\frac{7}{100}$10+8+910+7100

##### Question 7

Evaluate: Express $0.482$0.482 as the sum of integers and fractions. Fractions do not need to be simplified.

Think: Remember the place value of each number.

Do: $\frac{4}{10}+\frac{8}{100}+\frac{2}{1000}$410+8100+21000

#### More Worked Examples

##### Question 1

Write the decimal $0.2$0.2 as a fraction in its simplest form.

##### Question 2

Write the decimal $0.26$0.26 as a fraction in its simplest form.

##### Question 3

Write the decimal $1.856$1.856 as a simplified improper fraction.

##### Question 4

Express the following as the sum of integers and fractions that show the place value of each digit: $1.416$1.416

Fractions need not be simplified. For example: $23.5=20+3+\frac{5}{10}$23.5=20+3+510