Dividing Decimals

1. Section 5.4 Dividing Decimals

2. quotient divisor dividend 52.92 63 Division of decimal numbers is similar to division of whole numbers. The only difference is the placement of a decimal point in thequotient. 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. 0 8 4 -504 25 2 -252 0

3. divisor dividend 6 3 . 52 . 92 63 . 529 . 2 63 52 9.2 If the divisor isnota whole number, we need to move the decimal point to the right until the divisor is a whole number before we divide. 8 4 - 504 25 2 -252 0 Martin-Gay, Prealgebra, 5ed

4. 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 numberofplaces 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. Martin-Gay, Prealgebra, 5ed

5. Estimating When Dividing Decimals Divide 258.3 ÷ 2.8 Exact Estimate rounds to This is a reasonable answer. Martin-Gay, Prealgebra, 5ed

6. 456.2 = 45 . 62 10 1 zero 456.2 = 0 . 4562 1 , 000 3 zeros There are patterns that occur when dividing by powers of 10, such as 10, 100, 1000, and so on. The decimal point moved 1 place to the left. The decimal point moved 3 places to the left. The pattern suggests the following rule. Martin-Gay, Prealgebra, 5ed

7. Notice that this is the same pattern as multiplying by powers of 10 such as 0.1, 0.01, or 0.001. Because dividing by a power of 10 such as 100 is the same as multiplying by its reciprocal , or 0.01. To divide by a number is the same as multiplying by its reciprocal. Dividing Decimals by Powers of 10 such as 10, 100, or 1000, . . . Move the decimal point of the dividend to theleftthe same number of places as there are zerosin the power of 10.