Algebra I Recipe: Scientific Notation
By G Redden
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A. Writing Scientific Notation into Decimal Form
- If the exponent is positive, move the decimal to the right that many times.
- If the exponent is negative, move the decimal to the left that many times.
3.203 x 104
2.42 x 10-4
5.003 x 102
9.81 x 10-1
B. Writing Decimals into Scientific Notation
- The first number must be ≥ 1 but < 10.
- If the decimal is moved to the left, then the exponent will be positive – the number of times the decimal is moved.
- If the decimal is moved to the right, then the exponent will be negative – the number of times the decimal is moved.
386.27
0.004258
3,902,000
0.0000000234
C. Multiplying and Dividing Numbers in Scientific Notation
- Multiply or divide the "coefficient numbers."
- Multiply or divide the like bases of 10.
- If the answer is not in scientific notation, move the decimal appropriately.
- If the "coefficient number" becomes larger after moving the decimal, decrease the exponent by the number of times the decimal is moved.
- If the "coefficient number" becomes smaller after moving the decimal, increase the exponent by the number of times the exponent is moved.
(1.27 Ă— 10-6)(9.35 Ă— 102)
(8.31 Ă— 1014)(7.16 Ă—10-5)
(2.13 Ă— 10-7) / (9.26 Ă— 103)
(3.57 Ă— 1012) / (8.44 Ă— 10-4)
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