Section 5.4 Multiplying Signed Decimal Numbers

1. Section 5.4 Multiplying Signed Decimal Numbers • Steps for Multiplying Decimals • 1. Ignore decimals and multiply as before • 2. Count the number of digits after the decimal in the original problem and make sure the answer has the same number of digits after the decimal.

2. Simplify the following: 1. 0.07(0.03) 2. –0.42(6) 7 ( 3 ) - 42 ( 6 ) 21 - 252 4 decimal places 2 decimal places -2.52 0.0021

3. 3. 3.12(0.05) 4. –0.02(–1.39) 312 ( 5 ) - 2 ( -139 ) 1560 278 4 decimal places 4 decimal places 0.0278 0.1560

4. 5. 1.22 6. (- 0.3)2 1.2 ( 1.2 ) - 0.3 ( - 0.3 ) 12 ( 12 ) - 3 ( - 3 ) 144 9 0.09 1.44

5. 7. 0.5(22) 8. 10(.314) 5 ( 22 ) 10 ( 314 ) 3140 110 11.0 3.14

6. 9. 100(.314) 10. 1000(.314) 100 ( 314 ) 1000 ( 314 ) 314000 31400 31.4 314

7. 11. What is the perimeter of a rectangular field that measures 4.2 miles by 3.1 miles? P = 2l + 2w P = 2(4.2) + 2(3.1) P = 2(42) + 2(31) P = 84 + 62 8.4 + 6.2 P = 8.4 + 6.2 The perimeter of the rectangular field is 14.6 miles.

8. 12. What is the area of a rectangular field that measures 4.2 miles by 3.1 miles? A = bh A = (4.2)(3.1) A = (42)(31) A = 1302 A = 13.02 The area of the rectangular field is 13.02 square miles.

9. 13. John worked 63.5 hours over the past two weeks. John earns $9.50 per hour. How much money did John earn? John’s earnings = (63.5)(9.50) John’s earnings = (635)(95) John’s earnings = 60325 John’s earnings = 603.25 John earned $603.25.

10. 14. Jill filled up the gas tank in her new hybrid car. Jill put 10.39 gallons of gas in her car at a rate of $2.39 per gallon. How much did she pay for gas? Gas Bill = (10.39)(2.39) Gas Bill = (1039)(239) Gas Bill = 248321 Gas Bill = 24.83 Jill purchased $24.83 worth of gas.

11. 15. What is the volume of a rectangular cube with dimensions 3.2 feet by 4.1 feet by 1.1 feet? Volume = (3.2)(4.1)(1.1) V = (32)(41)(11) V = 14432 V = 14.432 The volume of the rectangular cube is 14.432ft3.

12. Sec 5.4 Multiplying decimals Pg. 337 9 – 19 odd, 39 – 59 odd, 10, 16, 40, 48, 54

13. Section 5.5 Dividing Signed Decimal Numbers • Steps for dividing by whole numbers • Use long division as if there were no decimal point involved. • If necessary, add zeros after last digit in the decimal. • 3. Place decimal point directly above the decimal point in the problem.

14. Divide the following: 4 7 6 5 8 7 0 32 -28 5 2 -3 4 48 -32 -2 8 4 0 -28 40 0 0

15. Steps for dividing by decimals numbers 1. Change divisor to a whole number by moving both numbers the same amount of digits 2. Divide as before

16. 6 6 6 Divide the following: 198 21 7 198 19 8 198 0

17. Divide the following: 3 3 66 6 6 66 0

18. 5. .3778 ÷ .25 and round to the nearest hundredth: When rounding make sure to calculate one digit past required place value. 1 5 1 1 1.51 0 25 12 7 125 2 8 25 3 0 25

19. 6. 4.579 + 34.8 ÷ (–4) -8 7 4.579 + 34.8 ÷ (–4) 32 4.579 + ( -8.7 ) 2 8 28 0 - 8.700+4.579 -4.121

20. 7. (3.07 – 0.43) ÷ 0.33 3.07 – 0.43 (3.07 – 0.43) ÷ 0.33 2.64 2.64 ÷ 0.33 8 8 264 0

21. 0.3 (0.3) 8. 6 – (0.3)2 ÷ 10 3 (3) 6 – (0.3)2 ÷ 10 9 6 – 0.09 ÷ 10 0.09 6 – 0.09÷ 10 0 0 9 6 – 0.009 0 6 – 0.009 .000 90 0 5.991

22. 9. Jill filled up the gas tank in her new hybrid car. Jill put 10.3 gallons of gas in her car and she had driven 473.8 miles. Estimate the gas mileage then determine how many miles per gallon her car achieved? 47 mpg 470 miles ÷ 10 gallons

23. 9. Jill filled up the gas tank in her new hybrid car. Jill put 10.3 gallons of gas in her car and she had driven 473.8 miles. Estimate the gas mileage then determine how many miles per gallon her car achieved? 47 mpg 4 6 Jill can get 46 miles per gallon while driving her hybrid car. 412 61 8 618 0

24. Sec 5.5 Dividing decimals Pg. 349 1 – 6 all, 9, 10, 12, 15, 35 – 59 odd, 42, 60