Math Core

Which is more, $0.6$ or $0.58$ ? Many people pick $0.58$ because it has more digits. But that is wrong! Place value tells you how to compare decimals the right way.

Compare place by place

Line up the decimal points, then compare the digits from left to right: ones first, then tenths, then hundredths. The first place where the digits are different decides which number is greater.

	Ones	Tenths	Hundredths
$0.6$	0	6	0
$0.58$	0	5	8

The ones are the same (0 and 0). In the tenths place, 6 is greater than 5. So $0.6$ is greater. You don't even need to look at the hundredths. We write $0.6 > 0.58$ .

Add a zero to make them match

Putting a 0 at the end of a decimal does not change its value, because $0.6$ and $0.60$ both mean 6 tenths (or 60 hundredths). So you can rewrite the numbers with the same number of digits:

0.6 = 0.60 \qquad \text{and} \qquad 60 \text{ hundredths} > 58 \text{ hundredths}

Money shows it too: 60 cents is more than 58 cents.

Use a number line

On a number line, the number farther to the right is greater. Here $0.58$ is to the left of $0.6$ :

How to compare decimals

Line up the decimal points. Add zeros at the end so both numbers have the same number of digits.
Compare the digits from left to right.
The first place where the digits differ tells you which number is greater.

Common mistake

More digits does not mean bigger. $0.3$ is greater than $0.25$ , because 3 tenths is 30 hundredths, and 30 hundredths is more than 25 hundredths.

Worked example: Tenths only

Compare $0.7$ and $0.4$ using $>$ , $<$ or $=$ .

Both have 0 ones. In the tenths place, 7 is greater than 4. So $0.7 > 0.4$ .

Worked example: Different numbers of digits

Compare $3.45$ and $3.5$ .

Add a zero so both have two decimal places: $3.45$ and $3.50$ .

The ones match (3 and 3). In the tenths place, 4 is less than 5. So $3.45 < 3.5$ .

Worked example: Putting decimals in order

Order from least to greatest: $0.9$ , $0.09$ , $0.19$ , $0.91$ .

Write them all with two decimal places: $0.90$ , $0.09$ , $0.19$ , $0.91$ . Now compare them as hundredths: 90, 9, 19 and 91.

From least to greatest: $0.09$ , $0.19$ , $0.9$ , $0.91$ .

Worked example: Is it the same whole?

Ana ate $0.5$ of a small pizza. Ben ate $0.4$ of a large pizza. Can you tell who ate more pizza just by comparing $0.5$ and $0.4$ ?

No. $0.5 > 0.4$ , but the two pizzas are different sizes. Four tenths of a very large pizza could be more food than five tenths of a small one. Comparing decimals only tells you who ate more when both decimals are parts of the same whole.

Tip

Think of decimals as money. $0.6$ is like $0.60 and $0.58$ is like $0.58. Which would you rather have?

Practice

Practice 1

Which symbol makes this true? $0.8 \ \square \ 0.3$

Practice 2

Which symbol makes this true? $0.4 \ \square \ 0.40$

Practice 3

Which symbol makes this true? $0.72 \ \square \ 0.8$

Practice 4

Which symbol makes this true? $2.09 \ \square \ 2.1$

Practice 5

Which number is the greatest?

Practice 6

Sam jumped $1.6$ meters. Lee jumped $1.58$ meters. Who jumped farther?

Practice 7

Put these numbers in order from least to greatest: $1.3$ , $1.03$ , $1.33$ , $0.3$ .

Separate your answers with commas.

Separate answers with commas, e.g. 2, -5

Practice 8

Use each of the digits 2, 9 and 5 exactly once to fill in $\square.\square\square$ . What is the greatest number you can make?

Type a number.