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You cannot use the number of decimal places in the scientific notation unless both numbers have the same power of ten.

If the power of ten are different then you can use the number of decimal places in the actual number but that can sometimes be rather cumbersome: when a lot of zeros are involved. A better way is to alter one of the numbers so that both have the same power.

For example, to add 5.432*10^3 and 6.789*10^1 convert one of the numbers so that it has the same power as the other. Now both numbers have the same power. Add the mantissae of the two numbers and append the same exponent. You may have to adjust the answer to get back to scientific notation.

Thus, 5.432*10^3 + 6.789*10^1 = 543.2*10^1 + 6.789*10^1

= (543.2 + 6.789)*10^1

= 549.989*10^1

= 5.49989*10^3


5.432*10^3 + 6.789*10^1 = 5.432*10^3 + 0.06789*10^3

= (5.432 + 0.06789)*10^3

= 5.49989*10^3

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In addition and subtraction, you use the number of decimal places to determine significant figures.

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Q: When doing addition of numbers in scientific notation with significant figures do you use the number of decimal places in the scientific notation or in the actual number?
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