Here are the answers:
4 X 106 + 5 X 105 = 4,000,000 + 500,000 = 4,500,000 = 4.5 X 106
8.4 X 104 + 2.8 X 102 = 84,000 + 280 = 84,280 = 8.428 X 104
4.8 X 10-5 + 7.5 X 10-4 = 0.000048 + 0.00075 = 0.000798 = 7.98 X 10-4
8.1 X 102 + 4 X 10-2 = 810 + 0.04 = 810.04 = 8.1004 X 102
It is difficult to see a pattern here, except that it seems that the answer will have an exponent similar to the larger exponent of the two numbers.
Adding and subtracting numbers in scientififc notation is much more difficult than multiplication and division. It is usually best to use a calculator, to avoid errors. However, if you don't have a calculator which does scientific notation, there is a process:
Determine which of the numbers has the smaller exponent.
Change this number by moving the decimal place to the left and raising the exponent, until the exponents of both numbers agree. Note that this will take the lesser number out of standard form.
Add or subtract the coefficients as needed to get the new coefficient.
The exponent will be the exponent that both numbers share.
Put the number in standard form.
Let's use the numbers above as examples of this process:
4 X 106 + 5 X 105 = 4 X 106 + 0.5 X 106 = (4 + 0.5) X 106 = 4.5 X 106
8.4 X 104 + 2.8 X 102 = 8.4 X 104 + 0.28 X 103 = 8.4 X 104 + 0.028 X 104 = (8.4 + 0.028) X 104 = 8.428 X 104
4.8 X 10-5 + 7.5 X 10-4 = 0.48 X 10-4 + 7.5 X 10-4
= (0.48 + 7.5) X 10-4 = 7.98 X 10-48.1 X 102 + 4 X 10-2 = 8.1 X 102 + 0.4 X 10-1 = 8.1 X 102 + 0.04 X 100
= 8.1 X 102 + 0.04 X 101 = 8.1 X 102 + 0.004 X 102 = (8.1 + 0.004) X 102
= 8.1004 X 102Now practice this technique:
1.5 X 104 + 5.4 X 105
4.46 X 10-7 + 5.9 X 10-5
8.4 X 1021 + 9.455 X 1024
5.14 X 104 - 2.49 X 102
8.45 X 1064 - 4.5 X 1063
8.46 X 107 - 7.94 X 109
7.54 X 103 + 6.49 X 102 +4.96 X 105 + 9.32 X 104
9.4 X 10-8 - 7.6 X 10-9+ 8.6 X 10-7
Check your answers
Questions? Ask the designer, Jim Heath
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