Multiplying Decimals: Count the Decimal Places

Quick answer

To multiply decimals, ignore the points and multiply as whole numbers. Then count the total decimal places in both factors and put that many into the answer. 0.3 times 0.4 is 12 with two decimal places, giving 0.12. Unlike adding, there is no need to line the points up, and the answer can be smaller than both numbers you started with.

What you'll learn

Multiply decimals by multiplying as whole numbers and placing the point
Explain why the decimal places in the factors are added
Multiply by powers of ten by moving the point

Ignore the points, then count them

Multiplying decimals is a whole-number multiplication with one extra step at the end.

Ignore the decimal points and multiply as whole numbers.
Count the decimal places in both factors and add them.
Put that many decimal places into the answer.

0.3 \times 0.4 \quad\longrightarrow\quad 3 \times 4 = 12 \quad\longrightarrow\quad 0.12

One place plus one place is two places, so $12$ becomes $0.12$ .

Why the places add

This is the part usually presented as a rule to memorise. It follows from what a decimal place is.

A decimal place is a division by ten. So

0.3 = \frac{3}{10} \qquad 0.4 = \frac{4}{10}

Multiplying them multiplies the tops and the bottoms:

\frac{3}{10} \times \frac{4}{10} = \frac{12}{100} = 0.12

Two tens on the bottom means dividing by a hundred, which is two decimal places. Dividing by ten twice is dividing by a hundred — that is the whole reason the counts add rather than doing anything more complicated.

Why the answer can shrink

$0.3 \times 0.4 = 0.12$ , which is smaller than either factor. That looks wrong until you read it as “of”:

Three tenths of four tenths is a small part of an already small amount.

Multiply by	The answer
more than $1$	grows
exactly $1$	unchanged
less than $1$	shrinks

The same rule you met in multiplying fractions, because decimals are fractions.

Powers of ten move the point

Multiplying by $10$ , $100$ or $1000$ needs no working at all — the point moves right by one place per zero.

Calculation	Answer	Point moved
$4.7 \times 10$	$47$	one right
$4.7 \times 100$	$470$	two right
$0.056 \times 1000$	$56$	three right

Each place is worth ten times the one to its left, so multiplying by ten promotes every digit one place. Dividing sends them the other way.

Checking the size

Before trusting an answer, estimate. Round each factor to a friendly whole number and multiply those.

3.9 \times 5.2 \quad\approx\quad 4 \times 5 = 20

An answer of $20.28$ is plausible; $2.028$ or $202.8$ are not. This catches a misplaced point instantly, which is the dominant error here.

Worked examples

Common mistakes

Practice problems

Work out $0.4 \times 0.2$ .

Answer

$0.08$

Full solution

$4 \times 2 = 8$ , and $1 + 1 = 2$ places, so the answer is $0.08$ .
Work out $0.5 \times 0.6$ .

Answer

$0.3$

Full solution

$5 \times 6 = 30$ , and two places gives $0.30$ , which is $0.3$ .
Work out $2.4 \times 3$ .

Answer

$7.2$

Full solution

$24 \times 3 = 72$ , and $1 + 0 = 1$ place, so $7.2$ .
Work out $1.2 \times 0.5$ .

Answer

$0.6$

Full solution

$12 \times 5 = 60$ , and $1 + 1 = 2$ places gives $0.60$ , which is $0.6$ .
Work out $0.03 \times 0.6$ .

Hint

Three places, and only one significant digit.

Answer

$0.018$

Full solution

$3 \times 6 = 18$ , and $2 + 1 = 3$ places, so the answer is $0.018$ .
Work out $6.35 \times 10$ .

Answer

$63.5$

Full solution

One zero, so the point moves one place right.
Work out $0.008 \times 1000$ .

Answer

$8$

Full solution

Three zeros, so the point moves three places right, landing after the $8$ .
Work out $4.5 \times 2.2$ .

Answer

$9.9$

Full solution

$45 \times 22 = 990$ , and $1 + 1 = 2$ places gives $9.90$ , which is $9.9$ .

Estimate check: about $4.5 \times 2 = 9$ ✓
A tap fills $1.75$ litres a minute. How much in $6.4$ minutes?

Answer

$11.2$ litres

Full solution

$175 \times 64 = 11200$ , and $2 + 1 = 3$ places gives $11.200$ , which is $11.2$ litres.

Estimate check: about $2 \times 6 = 12$ ✓
Leo works out $0.5 \times 0.5$ and gets $2.5$ . Find his error.

Hint

Should the answer be bigger or smaller than $0.5$ ?

Answer

He seems to have divided rather than multiplied, and lost the places. The answer is $0.25$ .

Full solution

Both factors are below $1$ , so the answer must be smaller than either of them. An answer of $2.5$ is five times bigger than $0.5$ , which fails the check before any working is rechecked.

Correctly: $5 \times 5 = 25$ , and $1 + 1 = 2$ places, so $0.5 \times 0.5 = 0.25$ .

Half of a half is a quarter, which is exactly what $0.25$ says.

Frequently asked questions

How do I multiply decimals?

Ignore the decimal points and multiply as whole numbers. Then count the decimal places in both factors, add them, and put that many decimal places into the answer.

Do I line up the decimal points like I do for adding?

No. Alignment matters for adding because columns must hold matching places. Multiplication does not work column by matching column, so the points are irrelevant until the very end.

Why do the decimal places add?

Because each decimal place is a division by ten. One place plus one place means dividing by ten twice, which is dividing by a hundred — so the answer has two places.

Why is 0.3 times 0.4 smaller than both?

Multiplying by a number below 1 takes a part of something, and a part is smaller than the whole. Three tenths of four tenths is a small slice of an already small amount.

How do I multiply by 10 or 100?

Move the decimal point one place right for each zero. Times 10 moves it one place, times 100 moves it two. Dividing moves it the other way.

What to learn next

Dividing Decimals: Move the Point, Then DivideHow to divide by a decimal by shifting both numbers until the divisor is whole, why that shift is allowed, and how to divide a decimal by a whole number.

Standards alignment

This lesson covers the following Common Core State Standards for Mathematics.

CCSS.MATH.CONTENT.5.NBT.B.7Number and Operations in Base TenAdd, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
CCSS.MATH.CONTENT.6.NS.B.3The Number SystemFluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
CCSS.MATH.CONTENT.5.NBT.A.2Number and Operations in Base TenExplain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

For teachersPrint problems onlyTick to print a blank worksheet; leave it clear to print the lesson with the full answer key.

Quick answer

What you'll learn

Frequently asked questions

How do I multiply decimals?

Do I line up the decimal points like I do for adding?

Why do the decimal places add?

Why is 0.3 times 0.4 smaller than both?

How do I multiply by 10 or 100?

What to learn next

Standards alignment

More Decimals lessons