DECIMAL
ARITHMETIC
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....
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 !
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
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 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
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
Quick Exercises
1) 0.79 + 0.16
2) 0.78 – 0.34
3) 0.88 + 0.114
4) 0.721 – 0.056
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
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
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)
Quick Exercise
1) 1.034 x 0.89
2) 0.965 x 0.045
3) 0.12 / 0.04
4) 1.32 / 0.1
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
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