Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product.

0.7 0.03 = 7

10

3

100

1 decimal place

2 decimal places

21

1000

= 0.021

=

3 decimal places

Multiplying Decimals

Step 1: Multiply the decimals as though they were whole numbers.

Step 2: The decimal point in the product is placed so the number of decimal places in the product is equal to the sum of the number of decimal places in the factors.

Multiplying Decimals

Examples1 Multiply: 6.78 × 0.05372 Multiply: 914.23 × 0.0132

The only difference is the placement of a decimal point in the quotient. If the divisor is a whole number, divide as for whole numbers; then place the decimal point in the quotient directly above the decimal point in the dividend.

8

- 5 0 4

2 52

-2 52

0

divisor

quotient

dividend

0 4

Division of decimal numbers is similar to division of whole numbers.

63 52.92

Dividing by a Decimal

8

63 52 9.2

- 504

25 2

-252

0

4

If the divisor is not a whole number, we need to move the decimal point to the right until the divisor is a whole number before we divide.

divisor dividend6 3 52 92. .

63 529 2. .

Dividing by a Decimal

Dividing by a Decimal

Step 1: Move the decimal point in the divisor to the right until the divisor is a whole number.

Step 2: Move the decimal point in the dividend to the right the same number of places as the decimal point was moved in Step 1.

Step 3: Divide. Place the decimal point in the quotient directly over the moved decimal point in the dividend.

Examples3 Divide: 0.084 ÷ 0.354 Divide and round to two decimal places:

0.004415 ÷ 0.032

Estimating sums, differences, products, and quotients of decimal numbers is an important skill whether you use a calculator or perform decimal operations by hand.

Estimating Operations on Decimals

Add 23.8 + 32.1.

Estimating When Adding Decimals

Exact Estimate

23.8+32.1

55.9

rounds to 24rounds to 32

56

This is a reasonable answer.

When rounding to check a calculation, you may want to round the numbers to a place value of your choosing so that your estimates are easy to compute mentally.

Helpful Hint

Multiply 32.3 1.9.

Estimating when Multiplying Decimals

Exact Estimate

32.3

1.9

290.7323.061.37

rounds to 32rounds to 2

64

This is a reasonable answer.

Divide 258.3 ÷ 2.8

Estimating When Dividing Decimals

Exact Estimate

28. 2583. - 252 63 - 56 70 - 56 140 -140 0

rounds to 3 300100

This is a reasonable answer.

92.25

Examples5 Estimate, then evaluate: 44.612 × 2.146 Divide. Round to two decimal places. 52

÷ 18