Math Core

A fraction with a denominator of 10 or 100 can also be written as a decimal. They are two names for the same amount, just like "a quarter" and "25 cents." Knowing both names lets you pick whichever one makes a problem easier.

Fractions to decimals

The denominator tells you which place to use.

$\dfrac{7}{10}$ is 7 tenths, so it is $0.7$ .
$\dfrac{43}{100}$ is 43 hundredths, so it is $0.43$ .
$\dfrac{9}{100}$ is 9 hundredths. The 9 must be in the hundredths place, so you need a 0 in the tenths place: $0.09$ .

It works the other way too. $0.5$ is 5 tenths, which is $\dfrac{5}{10}$ . $0.18$ is 18 hundredths, which is $\dfrac{18}{100}$ .

Decimals and fractions

A fraction out of 10 becomes a decimal with one digit after the decimal point: $\dfrac{3}{10} = 0.3$ .
A fraction out of 100 becomes a decimal with two digits after the decimal point: $\dfrac{3}{100} = 0.03$ and $\dfrac{31}{100} = 0.31$ .

Tenths are also hundredths

Every tenth is made of 10 hundredths. So 4 tenths is the same as 40 hundredths:

\frac{4}{10} = \frac{4 \times 10}{10 \times 10} = \frac{40}{100}

In decimals, that means $0.4 = 0.40$ . Both land on the same spot on a number line:

0.4 and 0.40 are the same point

Mixed numbers

A mixed number has a whole part and a fraction part. The whole part goes to the left of the decimal point.

$3\dfrac{6}{10} = 3.6$
$2\dfrac{5}{100} = 2.05$

Adding tenths and hundredths

To add a fraction out of 10 to a fraction out of 100, first rename the tenths as hundredths. Then add.

\frac{3}{10} + \frac{4}{100} = \frac{30}{100} + \frac{4}{100} = \frac{34}{100}

As a decimal, the sum is $0.34$ .

Common mistake

Don't mix up tenths and hundredths. $\dfrac{3}{100}$ is $0.03$ , not $0.3$ . And $0.5$ is $\dfrac{5}{10}$ , not $\dfrac{5}{100}$ . Count the digits after the decimal point: one digit means tenths, two digits means hundredths.

Worked example: Decimals to fractions

Write $0.8$ and $0.08$ as fractions.

$0.8$ has one digit after the decimal point, so it is 8 tenths: $\dfrac{8}{10}$ .

$0.08$ has two digits after the decimal point, so it is 8 hundredths: $\dfrac{8}{100}$ .

Worked example: A mixed number

A puppy weighs $5\dfrac{27}{100}$ kilograms. Write this as a decimal.

The whole number 5 goes before the decimal point. $\dfrac{27}{100}$ is 27 hundredths, which fills the tenths and hundredths places. The puppy weighs $5.27$ kilograms.

Worked example: Renaming tenths

Fill in the blank: $\dfrac{3}{10} = \dfrac{?}{100}$ .

Each tenth is 10 hundredths, so multiply the top and bottom by 10:

\frac{3}{10} = \frac{3 \times 10}{10 \times 10} = \frac{30}{100}

The missing number is $30$ .

Worked example: Adding

Add $\dfrac{6}{10} + \dfrac{25}{100}$ . Write the sum as a fraction and as a decimal.

Rename $\dfrac{6}{10}$ as $\dfrac{60}{100}$ . Then add the hundredths:

\frac{60}{100} + \frac{25}{100} = \frac{85}{100} = 0.85

Tip

Money makes a quick check. $\dfrac{85}{100}$ of a dollar is 85 cents, or $0.85.

Practice

Practice 1

Write $\dfrac{9}{10}$ as a decimal.

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Practice 2

Write $0.61$ as a fraction.

Type your answer like 3/100.

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Practice 3

Which decimal equals $\dfrac{7}{100}$ ?

Practice 4

Fill in the blank: $\dfrac{8}{10} = \dfrac{?}{100}$ .

Type a number.

Practice 5

Write $4\dfrac{3}{10}$ as a decimal.

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Practice 6

A ribbon is $3\dfrac{7}{100}$ meters long. Write its length as a decimal.

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Practice 7

Add $\dfrac{2}{10} + \dfrac{45}{100}$ .

Type your answer as a fraction out of 100, like 12/100.

Type a number.

Practice 8

Maya colors $\dfrac{3}{10}$ of a hundred grid red. Then she colors $\dfrac{16}{100}$ of the grid blue. What decimal of the grid is colored?

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