Decimals Explained: Tenths, Hundredths and Decimal Place Value

Q: Is 0.5 bigger than 0.45?

Yes. Compare place by place: 0.5 has 5 tenths and 0.45 has only 4 tenths, so 0.5 is bigger even though it has fewer digits.

Q: Why do you count decimal places when multiplying decimals?

Each decimal place is a division by 10. If the two numbers have three decimal places between them, their product has been divided by 1000, so the answer needs three decimal places.

How decimal places continue the base-ten pattern, how to compare decimals without being fooled by length, and how to add, subtract, multiply and divide them.

3 min read Supports 3 lessons

Place value does not stop at the units. Each place to the left is worth ten times more; each place to the right is worth ten times less. After the units come tenths, hundredths and thousandths, separated from the whole part by the decimal point.

3.472 = 3 + \frac{4}{10} + \frac{7}{100} + \frac{2}{1000}

Expanded form works exactly as it does for whole numbers.

$0.45$ sits halfway between $0.4$ and $0.5$ .

Comparing decimals

Compare decimals place by place from the left, just as you would whole numbers. The first place where they differ decides it.

Watch out

More digits does not mean bigger. $0.5 > 0.45$ , because $5$ tenths beats $4$ tenths. The extra digit in $0.45$ is only worth a few hundredths.

Tip

Pad with zeros so both decimals have the same length: $0.50$ against $0.45$ . Now it is like comparing $50$ with $45$ .

Adding and subtracting

Line up the decimal points so that tenths sit above tenths and hundredths above hundredths. Then add as usual.

\begin{aligned} 12.40& \\ +\;3.75& \\ \hline 16.15& \end{aligned}

Multiplying

Ignore the decimal points, multiply as whole numbers, then put back as many decimal places as the two numbers had between them.

$0.3 \times 0.12$
One decimal place, plus two decimal places.

1/4

This works because $0.3 = \frac{3}{10}$ and $0.12 = \frac{12}{100}$ , so the product is $\frac{36}{1000}$ .

Dividing by a decimal

Dividing by a decimal is awkward, so get rid of it. Multiply both numbers by the same power of ten until the divisor is a whole number. The answer does not change, for the same reason equivalent fractions work.

Dividing by a decimal

\frac{4.8}{0.06} = \frac{480}{6} = 80

Multiply top and bottom by $100$ .

Decimals and fractions

Every decimal that stops is a fraction over a power of ten: $0.35 = \frac{35}{100} = \frac{7}{20}$ . Going the other way, divide the numerator by the denominator: $\frac{3}{8} = 3 \div 8 = 0.375$ .

Some fractions never stop: $\frac{1}{3} = 0.333\dots$ repeats for ever. That is why fractions are often the more exact way to write an answer.

Common questions

Is 0.5 bigger than 0.45?: Yes. Compare place by place: $0.5$ has $5$ tenths and $0.45$ has only $4$ tenths, so $0.5$ is bigger even though it has fewer digits.
Why do you count decimal places when multiplying decimals?: Each decimal place is a division by $10$ . If the two numbers have three decimal places between them, their product has been divided by $1000$ , so the answer needs three decimal places.

Practise decimals

The Decimals & Place Value lesson has worked examples and unlimited practice that adapts to you.

Open the lesson

Common questions

Is 0.5 bigger than 0.45?

Yes. Compare place by place: $0.5$ has $5$ tenths and $0.45$ has only $4$ tenths, so $0.5$ is bigger even though it has fewer digits.

Why do you count decimal places when multiplying decimals?

Each decimal place is a division by $10$ . If the two numbers have three decimal places between them, their product has been divided by $1000$ , so the answer needs three decimal places.