1. Multiplying Decimals
Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product. 7 10 3
100  21
1000
0.7  = =
1 decimal place
2 decimal places =
3 decimal places

2. Chapter 1 / Whole Numbers and Introduction to Algebra
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.

3. Examples
Multiply: ×
Multiply: ×

4. Dividing by a Decimal
Division of decimal numbers is similar to division of whole numbers.
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 4
quotient
divisor 63
52.92
dividend
2 5 2
-2 52

5. Dividing by a Decimal
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 6 3 52 92 .
dividend 63
529 2 . 8 4 63 52
9.2
- 504 25 2
-252

6. Chapter 1 / Whole Numbers and Introduction to Algebra
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.

7. Examples Divide: 0.084 ÷ 0.35 Divide and round to two decimal places:
÷ 0.032

8. Chapter 1 / Whole Numbers and Introduction to Algebra
Estimating Operations on Decimals
Estimating sums, differences, products, and quotients of decimal numbers is an important skill whether you use a calculator or perform decimal operations by hand.

9. Chapter 1 / Whole Numbers and Introduction to Algebra
Estimating When Adding Decimals
Add
Exact
Estimate
rounds to
rounds to
This is a reasonable answer.

10. Chapter 1 / Whole Numbers and Introduction to Algebra
Helpful Hint
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.

11. Chapter 1 / Whole Numbers and Introduction to Algebra
Estimating when Multiplying Decimals
Multiply 32.3  1.9.
Exact
Estimate
rounds to
rounds to
This is a reasonable answer.

12. Chapter 1 / Whole Numbers and Introduction to Algebra
Estimating When Dividing Decimals
Divide ÷ 2.8
Exact
Estimate
rounds to
This is a reasonable answer.

13. Examples Estimate, then evaluate: 44.612 × 2.14
Divide. Round to two decimal places. 52 ÷ 18