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# Math 009 Unit 4 Lesson 1

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1. Math 009 Unit 4 Lesson 1

2. Obj: To write decimals in words thousandths ten-thousandths and tenths hundredths ones hundreds tens · 1 5 1 5 7 15.157 Fifteen and one hundred fifty-seven thousandths

3. Obj: To write decimals in words thousandths ten-thousandths and tenths hundredths ones hundreds tens · 3 0 6 0 0 1 7 306.0017 Three hundred six and seventeen ten-thousandths

4. Obj: To write words as decimals thousandths ten-thousandths and tenths hundredths ones hundreds tens · 5 3 8 Five and thirty-eight hundredths Answer: 5.38

5. Obj: To write words as decimals thousandths ten-thousandths and tenths hundredths ones hundreds tens · 1 9 0 0 4 Nineteen and four thousandths Answer: 19.004

6. Obj: To write words as decimals thousandths ten-thousandths and tenths hundredths ones hundreds tens · 0 0 0 7 1 Seventy-one ten-thousandths Answer: 0.0071

7. Naming place values: Name the place value of the digit 7 56.03789 263.893475 46.759834 thousandths hundred-thousandths tenths

8. Ordering decimal numbers Place the correct symbol between the two numbers Line up the decimals 7.6005 7.605 < 7.6005 7.605 Write the following numbers in order from smallest to largest 0.24, 0.024, 0.204, 0.0024 0.024 0.0024 0.24 0.024 0.204 0.0024 Answer: 0.24 0.204 0.0024, 0.024, 0.204, 0.24

9. Obj: To round a decimal to a given place value. Round 4.349254 to the nearest hundredth » 4.35 4.349254 Round 4.349254 to the nearest ten-thousandth » 4.3493 4.349254

10. Obj: To round a decimal to a given place value. Round 4.349254 to the nearest tenth » 4.3 4.349254 Round 15.0538 to the nearest hundredth » 15.05 15.0538 Round 15.0538 to the nearest tenth » 15.1 15.0538

11. Operations on decimals

12. Obj: To add decimals without a calculator • Write the numbers so that the decimals points are on a vertical line • add the columns just as you would with whole numbers Example: Find the sum of 42.3, 65.0729 and 162.903 1 1 1 42.3 65.0729 162.903 + 9 70.2759 0.2759 .2759 759 59 270.2759 Answer: 270.2759

13. Obj: To subtract decimals without a calculator • Write the numbers so that the decimals points are on a vertical line • subtract the columns just as you would with whole numbers Example: Subtract 39.047 and 7.96 14 8 9 39.047 – 7.96 270.2757 270.2787 270.087 231.087 231.087 Answer: 31.087

14. Find the following sums or differences 1. -31.894 + 7.5 = -24.394 2. -1.09 – (-8.3) = -1.09 + 8.3 = 9.39 3. -5.6 – (-3.82) – 17.409 = -5.6 + 3.82 – 17.409 = -19.189 4. How much greater is -31 than -62.09 ? -31 – (-62.09) = -31 + 62.09 = 31.09

15. Obj: To solve application problems involving decimals Find the missing length on the shaft 8.6 cm 2.77 cm ? 3.2 cm Solution: 2.77 + 3.2 = 5.97 missing length = 8.6 – 5.97 missing length = 2.63 cm

16. Obj: To solve application problems involving decimals Grace owned 357.448 shares of a mutual fund on January 1. On December 31 of the same year she noticed that her shares had increased by 82.469 shares. What was her new total at the end of that year? Solution: New Total = 357.448 + 82.469 = 439.917 shares

17. Estimate by rounding; then find the exact answer 6.272 – 1.848 Estimation: 6 – 2 = 4 Exact answer: 6.272 – 1.848 = 4.424 Evaluate x – y when x = 6.029 and y = - 4.708 x – y = 6.029 – (-4.708) = 6.029 + 4.708 = 10.737

18. Obj: To multiply decimals without a calculator • multiply the numbers as if they were whole numbers • the number of decimal places in the answer is the sum of the decimal places in the factors Multiply: 0.000086 x 0.057 Total decimal places in the factors is 9 0.000086 0.057 x 602 430 Total decimal places in the answer is 9 00000 4902 ^ Answer: 0.000004902

19. Obj: To divide decimals without a calculator Divide: 420.9 ¸ 7.06 Round your answer to the nearest tenth 5 9 6 1 · 7.06 420.9 0 706 42090. 00 ^ ^ 3530 » 59.6 Answer 679 0 6354 0 436 423 6 12 4 0 7 06

20. Do the following multiplications and divisions (0.72)(-3.7) -5.2(-0.8) -0.074 (10,000) 27.08 ¸ (-0.4) 58.37 ¸ 1000 = - 2.664 = 4.16 = - 740 = - 67.7 = 0.05837

21. Do the following multiplications and divisions Round answers to the nearest hundredth (5.78)(-3.799) -(18.47)(2.003) 8.57 ¸ 0.949 27.08 ¸ (-3.14) = 21.95822 »21.96 = -36.99541 »- 37.00 = 9.030558483 »9.03 = -8.624203822 »-8.62

22. Obj: To multiply decimals by powers of 10 • move the decimal point to the right the same number of places as the number of zeros in the power of 10 Multiply: 0.4207 x 1000 .4207 x 1000 = 4207 = 420.7 ^ Multiply: 63.75 x 10,000 63.75 x 10,000 = 6375 00 = 637,500 ^

23. Obj: To multiply decimals by powers of 10 • if the power of 10 is written in exponent form • move the decimal point to the right the same number of places as the power of 10 Multiply: 0.00006835 x 103 .00006835 x 103 = 00006835 = 0.06835 ^ Multiply: 4.68 x 105 4.68 x 105 = 468 000 = 468,000 ^

24. Obj: To divide decimals by powers of 10 • move the decimal in the dividend to the left the same number of places as the power of 10 (same number of places as the number of zeros) Divide: 58.3 ¸ 103 58.3 ¸ 103 = 0583 = 0.0583 ^ Divide: 0.625 ¸ 100 0.625 ¸ 100 = 00625 = 0.00625 ^

25. Obj: To convert fractions to decimals • divide the numerator by the denominator • place a bar over repeating digits • round the decimal answer if necessary Convert to a decimal: 3 8 = 0.375 17 25 8 68 8. = 1 6 4 4.16 4. 1666… = =

26. Obj: To convert fractions to decimals Certain conversions from fractions to decimals should be memorized 14 = 0.25 13 = 0.333… = 0.3 12 = 0.5 23 = 0.666… = 0.6 34 = 0.75

27. Obj: Convert decimals to fractions • remove the decimal point • for a denominator use a power of ten that corresponds to the decimal places in the original number • reduce the fraction Convert fractions 7 35 = 0.35 = 20 100 11 275 = 0.275 = 40 1000 76 100 19 25 5 5 5.76 = =

28. Obj: Compare a decimal and a fraction • change the fraction to a decimal • compare the decimals Place the correct symbol, > or <, between the numbers 3 8 > 12 < 4.509 4 0.32 0.32 0.375 4.509 4.5 0.32 4.509 0.375 4.5 00

29. Checking a solution to an equation Is -1.2 a solution for 6.4 = 5.2 + x ? 6.4 = 5.2 + x 6.4 5.2 + (-1.2) 4 No , -1.2 is not a solution for the equation

30. Checking a solution to an equation Is -3.6 a solution for -9x = 32.4 ? -9x = 32.4 -9(-3.6) 32.4 32.4 Yes , -3.6 is a solution for the equation