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Problem-Solving Worksheet 4
Scientific Notation
To multiply two numbers written in scientific notation, first multiply the factors that are not
powers of 10. Then multiply the powers of 10 by adding their exponents. If the answer is not in
scientific notation, rewrite it in scientific notation. Remember to round your answer to the correct
number of significant figures.
Example 1
Multiply 3.7 x 102 by 5.1 x 103.
Solution
First multiply 3.7 by 5.1 to get 18.87. Then multiply 102 by 103 to get 105. Then round 18.87 x 105
to two significant figures and rewrite the answer in scientific notation. This gives 1.9 x 106.
To divide numbers written in scientific notation, first divide the factors that are not powers of 10.
Then divide the powers of 10 by subtracting exponents. If the answer is not in scientific notation,
rewrite it in scientific notation.
Example 2
Divide 2.3 x 10-3 by 4.6 x 10-6
Solution
Divide 2.3 by 4.6 and ID-3 by 10-6 This gives 0.50 x 10 -3-(-6) = 0.50 x 103
In scientific notation, the answer is 5.0 x 102.
To add or subtract numbers written in scientific notation, first change the numbers so that they are
both expressed to the same power of 10. Then add or subtract the factors. The exponent does not
change for an addition or subtraction. If your answer is not in scientific notation, rewrite it in
scientific notation.
Example 3
Add 9.67 x10 2 and 8.5 x103.
Solution
First convert the numbers so that the powers of 10 are the same. For example, change 8.5 x 103 to 85
x 102. Then add. This gives 94.67 x 102. This is not in scientific notation; rewrite it as 9.467 x 103.
Rounding to the tenths place (because 8.5 x 103 is the least exact number in the calculation) gives
9.5 x 103Example 4
Subtract 8.08 x 10-6 from 2.07 x 10-5.
Solution
First convert the numbers so that the powers of 10 are the same. For example, change 2.07 x 10-5 to
20.7 x 10-6. Then subtract. This gives 12.62 x 10-6. In scientific notation, this is 1.262 x 10-5.
Rounding to the hundredths place (because 2.07 x 10-5 is the least exact number in the calculation) gives
1.26 x 10-5.
Exercises
Express each of the following numbers in scientific notation.
1. 239,000,000,000 ___________________________________________
2. 0.0000158.
3. 738____
4. 0.020.
5.4200
Perform the calculations below. Then express your answers in scientific notation.
6. Multiply 7 x 10-3 by 1.2 x 109.
7. Divide 3.6 x 102 by 4.8 x 108.
9. Subtract 3.6 x 10-8 from 4.5 x 10-7
10. Multiply 7.2 x 10-2 by 5.1 x 10-3.
8. Add 8.75 x 104 to 2.513 x 105.
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Problem-Solving Skills 9