DECIMAL ARITHMETIC

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

Conversion To & Back From An Equivalent 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”) = x 10 x 10 (“2 Places”) = Multiply / Divide by 10 “moves” the point !

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

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

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

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

Quick Exercises 1) ) 0.78 – ) ) – 0.056

Answers To Quick Exercise 1) , 0.16 both x 100, = 95, /100 = ) 0.78 – , 0.34 convert to = 44, /100 = ) , convert to , /1000 = ) – – 56 = 665, / 1000 = 0.665

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

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

Quick Exercise 1)1.034 x )0.965 x )0.12 / )1.32 / 0.1

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

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