Math Core

A ribbon costs $0.75 per foot, and you need 3 feet. A garden bed is 2.5 meters long and 1.2 meters wide. To answer questions like these, you need to multiply decimals. You already know how to multiply whole numbers, and that does most of the work. The only new step is deciding where the decimal point goes.

A whole number times a decimal

Multiplying by a whole number is repeated addition, just like before. $3 \times 0.4$ means three groups of 0.4:

Three hops of 0.4 land on 1.2.

You can also think in place value words: 3 groups of 4 tenths is 12 tenths, and 12 tenths is $1.2$ . So $3 \times 0.4 = 1.2$ .

A tenth times a tenth

What is $0.3 \times 0.4$ ? Picture a square that is 1 unit on each side, cut into a 10 by 10 grid of 100 small squares. Each small square is one hundredth of the whole.

Shade a rectangle 3 tenths wide and 4 tenths tall. It covers $3 \times 4 = 12$ small squares. That is 12 hundredths, so

0.3 \times 0.4 = 0.12

Tenths times tenths makes hundredths, the same way tens times tens makes hundreds.

Counting decimal places

Look at the patterns:

Problem	Whole-number product	Decimal places in the factors	Answer
$3 \times 0.4$	$3 \times 4 = 12$	0 + 1 = 1	$1.2$
$0.3 \times 0.4$	$3 \times 4 = 12$	1 + 1 = 2	$0.12$
$2.5 \times 1.3$	$25 \times 13 = 325$	1 + 1 = 2	$3.25$

The digits come from the whole-number product. The number of decimal places in the answer is the total number of decimal places in the factors.

Multiplying decimals

Multiply as if there were no decimal points.
Count the digits after the decimal point in both factors, all together.
Place the decimal point so the answer has that many digits after the point.
Check with an estimate.

Worked example: A whole number times a decimal

Find $6 \times 0.35$ .

Multiply the whole numbers: $6 \times 35 = 210$ .
Decimal places: 6 has none and 0.35 has two. That is 2 in all.
Put 2 digits after the point: $2.10$ .

So $6 \times 0.35 = 2.10 = 2.1$ .

Estimate: 0.35 is a little more than one third, and $6 \times \dfrac{1}{3} = 2$ . The answer 2.1 makes sense.

Worked example: A decimal times a decimal

Find $2.5 \times 1.3$ .

Multiply the whole numbers: $25 \times 13 = 325$ .
Decimal places: one in 2.5 and one in 1.3. That is 2 in all.
Put 2 digits after the point: $3.25$ .

So $2.5 \times 1.3 = 3.25$ .

Estimate: $3 \times 1 = 3$ . The answer 3.25 is close, so the point is in the right spot.

Common mistake

When you need more decimal places than you have digits, write zeros in front. For $0.2 \times 0.3$ , the whole-number product is 6, and you need 2 decimal places. So the answer is $0.06$ , not $0.6$ . Think: 2 tenths of 3 tenths is 6 hundredths.

Worked example: A word problem with money

A ribbon costs $0.75 per foot. How much do 3 feet cost?

Find $3 \times 0.75$ . The whole-number product is $3 \times 75 = 225$ . There are 2 decimal places, so the answer is $2.25$ .

Three feet of ribbon cost $2.25.

Tip

Multiplying by a number less than 1 makes the answer smaller than the other factor. $0.5 \times 8 = 4$ , which is less than 8. If you multiply by a decimal less than 1 and get a bigger answer, check your decimal point.

Practice

Practice 1

Find $3 \times 0.2$ .

Type a number.

Practice 2

Find $6 \times 0.7$ .

Type a number.

Practice 3

Find $0.4 \times 0.8$ .

Type a number.

Practice 4

Find $2.3 \times 4$ .

Type a number.

Practice 5

What is $0.3 \times 0.2$ ?

Practice 6

Find $1.5 \times 2.4$ .

Type a number.

Practice 7

Nadia buys 4 bags of apples. Each bag costs $3.85. How much does she spend, in dollars?

Type a number.

Practice 8

A rug is 3.2 meters long and 1.5 meters wide. What is its area, in square meters?

Type a number.