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DECIMAL ARITHMETIC

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Equivalent Additions You may be asked to do the following sum without a calculator 0.87 + 0.57 How ? As we shall see throughout this work successful decimal arithmetic depends on manipulation to/from an EQUIVALENT SUM....

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Conversion To & Back From An Equivalent 0.87 + 0.57 Every time we multiply or divide by 10 the decimal point seems to “move” left or right 0.87 x 10 x 10 (“2 Places”) = 87.00 0.57 x 10 x 10 (“2 Places”) = 57.00 Multiply / Divide by 10 “moves” the point !

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Conversion To & From An Equivalent Original Sum 0.87 + 0.57 converted to 87 + 57 We MUST remember to divide the answer to the Equivalent Sum back by the same number of tens 87 + 57 = 144, divide by 100 (“2 Places”) Final Answer = 1.44

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Quick Fact Sheet Decimal arithmetic without a calculator requires conversion to / from whole numbers All decimal numbers in an addition or subtraction must be multiplied / divided by 10 the same number of times Multiplying and Dividing by 10 is like “moving” the decimal point

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Quick Examples Example Find 0.034 + 0.17 Look at the number with the highest number of decimal places and multiply both by this number of 10s. Eg. 0.034 has 3 decimal places so multiply both by 1000 (10x10x10) 0.034 x 1000 = 34, 0.17 x 1000 = 170 34 + 170 = 204, divide back by 1000 Answer: 0.204 Example Find 0.034 + 0.17 Look at the number with the highest number of decimal places and multiply both by this number of 10s. Eg. 0.034 has 3 decimal places so multiply both by 1000 (10x10x10) 0.034 x 1000 = 34, 0.17 x 1000 = 170 34 + 170 = 204, divide back by 1000 Answer: 0.204

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Quick Example Example 2 Find 0.917 – 0.82 Highest number of decimal places is 3 in 0.917 so multiply both by 10 x 10 x 10 (=1000) 0.917 x 1000 = 917, 0.82 x 1000 = 820 The converted sum is now 917 - 820 = 97 Divide back by 1000 to give the final answer 97 / 1000 = 0.097 Example 2 Find 0.917 – 0.82 Highest number of decimal places is 3 in 0.917 so multiply both by 10 x 10 x 10 (=1000) 0.917 x 1000 = 917, 0.82 x 1000 = 820 The converted sum is now 917 - 820 = 97 Divide back by 1000 to give the final answer 97 / 1000 = 0.097

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Quick Exercises 1) 0.79 + 0.16 2) 0.78 – 0.34 3) 0.88 + 0.114 4) 0.721 – 0.056

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Answers To Quick Exercise 1) 0.79 + 0.16 0.79, 0.16 both x 100, 79 + 16 = 95, /100 = 0.95 2) 0.78 – 0.34 0.78, 0.34 convert to 78 - 34 = 44, /100 = 0.44 3) 0.88 + 0.114 0.88, 0.114 convert to 880 + 114, /1000 = 0.994 4) 0.721 – 0.056 721 – 56 = 665, / 1000 = 0.665

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Multiplication Same principle of conversion to Equivalent Sums Find 1.076 x 0.08 (highest dp’s = 3) Convert to whole numbers 1.076 to 1076 (x 1000) and 0.08 to 80 (x 1000) 1076 x 80 = 86080 DIVIDE back by total number of tens 1000 x 100 = 10 x 10 x 10 x 10 x 10 x 10 (“6 Places”) 86080 / 100,000 = 0.086080

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Division Convert to whole numbers as usual using the highest number of decimal places Example Find 1.44 / 0.012 (3 dp’s) 1.44 x 1000 = 1440 and 0.012 x 1000 = 12 1440 / 12 = 120 (1000’s cancel top & bottom) Example Find 0.072 / 0.008 (3 dp’s) 0.072 x 1000 = 72 and 0.008 x 1000 = 8 72 / 8 = 9 (1000’s cancel top & bottom)

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Quick Exercise 1)1.034 x 0.89 2)0.965 x 0.045 3)0.12 / 0.04 4)1.32 / 0.1

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Multiplication & Division Answers 1)1.034 x 0.89 1.034,0.89 converted to 1034,890Final= 0.92026 2)0.965 x 0.045 0.965,0.045 converted 965,45 Final = 0.043425 3)0.12 / 0.04 Converted to 12,4 Final = 3 4) 1.32 / 0.1 Converted to 132, 10 Final = 13.2

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SUMMARY Decimal arithmetic without calculators requires conversions to whole numbers Decimals converted to whole numbers by Multiplication and Division by 10 Multiplying or Dividing by 10 seems like you are “moving” the decimal point SUMMARY Decimal arithmetic without calculators requires conversions to whole numbers Decimals converted to whole numbers by Multiplication and Division by 10 Multiplying or Dividing by 10 seems like you are “moving” the decimal point

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