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Math 009 Unit 4 Lesson 1 Obj: To write decimals in words 1 5 1 5 7 15.157 Fifteen and one hundred fifty-seven thousandths Obj: To write decimals in words 3 0 6 0 0 1 7 306.0017 Three hundred six and seventeen ten-thousandths Obj: To write words as decimals 5 3 8 Five and thirty-eight hundredths Answer: 5.38 Obj: To write words as decimals 1 9 0 0 4 Nineteen and four thousandths Answer: 19.004 Obj: To write words as decimals 0 0 0 7 1 Seventy-one ten-thousandths Answer: 0.0071 Naming place values: Name the place value of the digit 7 56.03789 thousandths 263.893475 hundred-thousandths 46.759834 tenths Ordering decimal numbers Place the correct symbol between the two numbers 7.6005 < 7.605 Line up the decimals 7.6005 7.605 Write the following numbers in order from smallest to largest 0.24, 0.024, 0.204, 0.0024 Answer: 0.24 0.024 0.024 0.0024 0.204 0.0024 0.0024, 0.024, 0.204, 0.24 0.24 0.204 Obj: To round a decimal to a given place value. Round 4.349254 to the nearest hundredth 4.349254 4.35 Round 4.349254 to the nearest ten-thousandth 4.349254 4.3493 Obj: To round a decimal to a given place value. Round 4.349254 to the nearest tenth 4.349254 4.3 Round 15.0538 to the nearest hundredth 15.0538 15.05 Round 15.0538 to the nearest tenth 15.0538 15.1 Operations on decimals 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 11 1 42.3 65.0729 162.903 70.2759 0.2759 .2759 759 599 270.2759 Answer: 270.2759 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 8 914 39.047 – 7.96 270.2787 270.2757 231.087 270.087 Answer: 31.087 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 Obj: To solve application problems involving decimals Find the missing length on the shaft 8.6 cm 2.77 cm Solution: ? 3.2 cm 2.77 + 3.2 = 5.97 missing length = 8.6 – 5.97 missing length = 2.63 cm 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 Estimate by rounding; then find the exact answer Estimation: 6.272 – 1.848 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 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 0.000086 x 0.057 602 430 000004902 ^ Total decimal places in the factors is 9 Total decimal places in the answer is 9 Answer: 0.000004902 Obj: To divide decimals without a calculator Divide: 420.9 7.06 Round your answer to the nearest tenth 5 96 1 7.06 0 00 706^ 420.9 42090. ^ 3530 6790 6354 436 0 423 6 12 4 0 7 06 Answer 59.6 Do the following multiplications and divisions (0.72)(-3.7) = - 2.664 -5.2(-0.8) = 4.16 -0.074 (10,000) = - 740 27.08 (-0.4) = - 67.7 58.37 1000 = 0.05837 Do the following multiplications and divisions Round answers to the nearest hundredth (5.78)(-3.799) = 21.95822 -(18.47)(2.003) = -36.99541 8.57 0.949 = 27.08 (-3.14) = 21.96 - 37.00 9.030558483 -8.624203822 9.03 -8.62 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 ^ 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 ^ Multiply: = 0.06835 4.68 x 105 4.68 x 105 = 468 000 = 468,000 ^ 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 = Divide: 0583 = 0.0583 ^ 0.625 100 0.625 100 = 00625 ^ = 0.00625 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 8 17 25 = 8. 68 4 1 6 = 4.1666… = 4.16 Obj: To convert fractions to decimals Certain conversions from fractions to decimals should be memorized 1 = 0.25 4 1 = 0.5 2 3 = 0.75 4 1 = 0.333… = 0.3 3 2 = 0.666… = 0.6 3 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 35 0.35 = 100 = 7 20 275 0.275 = 1000 = 11 40 76 19 5 5 5.76 = 100 = 25 Obj: Compare a decimal and a fraction • change the fraction to a decimal • compare the decimals Place the correct symbol, > or <, between the numbers 0.32 < 0.32 0.32 0.375 3 8 4.509 0.375 4.509 > 4.509 4.5 00 4 1 2 4.5 Checking a solution to an equation Is -1.2 a solution for 6.4 = 5.2 + x ? 6.4 = 6.4 5.2 + x 5.2 + (-1.2) 4 No , -1.2 is not a solution for the equation Checking a solution to an equation Is -3.6 a solution for -9x = 32.4 ? -9x -9(-3.6) = 32.4 32.4 32.4 Yes , -3.6 is a solution for the equation