4 Chapter Chapter 2 Decimals

Section 4.4 Dividing Decimals

Objective A Divide Decimals.

Dividing Decimals Dividing decimal numbers is similar to dividing whole numbers. The only difference is that we place a decimal point in the quotient. Dividing by a Whole Number Step 1: Place the decimal point in the quotient directly above the decimal point in the dividend. Step 2: Divide as with whole numbers. Objective A

Dividing by a Whole Number Dividing Decimals Dividing by a Whole Number Example Step 1: Place the decimal point in the quotient directly above the decimal point in the dividend. Step 2: Divide as with whole numbers. 5.9 Objective A 5

Example Divide: 219.2 ÷ 8. Check: quotient dividend divisor Objective A 6

Example Divide: 0.6 ÷ 4. Check: quotient divisor dividend Objective A 7

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. Objective A 8

Example Divide: 6.888 ÷ 2.8. 2.46 becomes Objective A 9

Estimate when Dividing Decimals. Objective B Estimate when Dividing Decimals.

Example Divide: 0.54 ÷ 12. Then estimate to whether the proposed result is reasonable. Estimate Exact Objective A The estimate is 0.05, so 0.045 is reasonable. 11

Divide Decimals by Powers of 10. Objective C Divide Decimals by Powers of 10.

Dividing Decimals by Powers of 10 There are patterns that occur when dividing by powers of 10, such as 10, 100, 1000, and so on. . 45 62 10 = 456.2 The decimal point moved 1 place to the left. 1 zero 1 000 4562 , . = 456.2 The decimal point moved 3 places to the left. 3 zeros The pattern suggests the following rule.

Dividing by Powers Dividing Decimals by Powers of 10 such as 10, 100 or 1000 Move the decimal point of the dividend to the left the same number of places there are zeros in the power of 10. Objective A 14

Examples Divide. a. b. = 0.5486 Move the decimal point 3 places to the left. Objective A = 0.068 Move the decimal point 1 place to the left. 15

Evaluate Expressions with Decimal Replacement Values. Objective D Evaluate Expressions with Decimal Replacement Values.

Example Evaluate x ÷ y for x = 0.035 and y = 0.02. Replace x with 0.35 and y with 0.02.

Solve Problems by Dividing Decimals. Objective E Solve Problems by Dividing Decimals.

Example A bag of fertilizer covers 1250 square feet of lawn. Tim Parker’s lawn measures 14,800 square feet. How many bags of fertilizer does he need? If he can buy only whole bags of fertilizer, how many whole bags does he need? bags = area of lawn ÷ amount bag covers Tim needs 12 bags of fertilizer.