Math Core

You already know fractions like $\dfrac{3}{10}$ . Decimals are another way to write parts of a whole. They use the same place value you use for big numbers, just going the other way: to the right of the ones place.

Tenths

Cut one whole into 10 equal parts. Each part is one tenth.

This strip has 10 equal squares. 3 of them are green.

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That is 3 tenths. As a fraction it is $\dfrac{3}{10}$ . As a decimal it is $0.3$ .

The dot is the decimal point. It separates the whole numbers (on the left) from the parts of a whole (on the right). The $0$ in front tells you there are no wholes.

Tenths live between 0 and 1 on a number line. Here the space from 0 to 1 is cut into 10 equal lengths, and the dot is 3 lengths from 0:

Hundredths

Now cut each tenth into 10 even smaller parts. The whole is split into $10 \times 10 = 100$ equal parts. Each one is one hundredth, written $0.01$ .

Money is a great way to picture this. A dollar is one whole.

A dime is one tenth of a dollar: $0.10.
A penny is one hundredth of a dollar: $0.01.

Here is the space from $0.2$ to $0.3$ cut into hundredths. The dot is at $0.26$ :

The place value chart

The number $2.47$ fits in a place value chart like this:

Ones	.	Tenths	Hundredths
2	.	4	7

It means 2 ones, 4 tenths and 7 hundredths. You read it as "two and forty-seven hundredths." The word and stands for the decimal point.

Places after the decimal point

The first place to the right of the decimal point is the tenths place.
The second place is the hundredths place.
Each place is worth 10 times the place to its right. So 10 hundredths make 1 tenth, and 10 tenths make 1 one.

Worked example: Counting money

Jo has 3 dollar bills, 4 dimes and 5 pennies. How much money is that?

3 dollars go in the ones place. 4 dimes are 4 tenths of a dollar. 5 pennies are 5 hundredths of a dollar.

Ones	.	Tenths	Hundredths
3	.	4	5

Jo has $3.45.

Worked example: Writing a decimal from words

Write "six and eight hundredths" as a decimal.

"Six" is the whole number, so write $6$ and then the decimal point. "Eight hundredths" means the 8 goes in the hundredths place. There are no tenths, so put a $0$ in the tenths place to hold it.

The answer is $6.08$ .

Common mistake

Watch the zero! $6.8$ is six and eight tenths. $6.08$ is six and eight hundredths. Always check which place each digit is in.

Worked example: Reading a number line

What decimal does the dot show?

The line goes from $0.7$ to $0.8$ in 10 equal steps, so each step is one hundredth. The dot is 3 steps past $0.7$ . It shows $0.73$ .

Tip

To check a decimal, say it out loud using place names. $0.73$ is "seventy-three hundredths," which matches $\dfrac{73}{100}$ .

Practice

Practice 1

The strip has 10 equal squares. What decimal is blue?

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Write your answer as a decimal, like 0.2.

Type your answer

Practice 2

What digit is in the hundredths place of $5.29$ ?

Type a number.

Practice 3

What decimal does the dot show?

Type your answer

Practice 4

Which decimal is "four and five hundredths"?

Practice 5

How many hundredths are the same as 3 tenths?

Type a number.

Practice 6

Leo has 2 dollar bills, 7 dimes and 3 pennies. How many dollars does he have? Write your answer as a decimal.

Type a number.

Practice 7

What decimal does the dot show?

Type a number.

Practice 8

What is the value of the 7 in $3.07$ ?