Mathematical Operations using Scientific Notation
Mathematical Operations using Scientific Notation
Addition and Subtraction
Examples: Add 4.2x103kg and 6.39x103kg.
In your calculator type 4.2EE3 + 6.39EE3=
Your answer on your calculator is 10590. However, this is not the correct answer because it is not in significant figures, and you are missing your unit. Remember the rules for addition says to line the numbers in columns and draw your line.
4.2 x103 kg
+ 6.39 x103 kg
10.59x103 kg
That would give you 10.6x103, but that is not in proper scientific notation form because the first number is not between 1 and 9.
The correct answer is 10600kg or 1.06x104kg (kg+kg=kg).
Multiplication
Example: Multiply 5.23x106mm by 7.1x10-2mm
In your calculator type 5.23EE6 x 7.1EE-2=
Your answer on your calculator is 371330. However, this is not the correct answer because it is not in significant figures, and you are missing your unit. Remember the rules for significant figures for multiplication says to use the lowest number of significant figures.
Since 5.23x106mm has 3 SF and 7.1x10-2mm has only 2 SF, your answer should only have two SF’s.
Your answer is 370000mm2 or 3.7x105mm2 (mm x mm=mm2). Remember zeros at the end of the number are not significant if there is no decimal.
Division
Example: Divide 5.44x107g by 8x104mol.
In your calculator type 5.44EE7 / 8EE4=
Your answer on your calculator is 680. However, this is not the correct answer because it is not in significant figures, and you are missing your unit. Remember the rules for significant figures for division says to use the lowest number of significant figures.
Since 5.44x107g has 3 SF and 8x104mol has 1 SF, your answer should only have one SF.
Your answer is 600g/mol or 6x102g/mol. Remember zeros at the end of the number are not significant if there is no decimal.
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