Algebra I Recipe: Scientific Notation
By G Redden
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.
1.
3.203 x 104
2.
2.42 x 10-4
3.
5.003 x 102
4.
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.
5.
386.27
6.
0.004258
7.
3,902,000
8.
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.
9.
(1.27 × 10-6)(9.35 × 102)
10.
(8.31 × 1014)(7.16 ×10-5)
11.
(2.13 × 10-7) / (9.26 × 103)
12.
(3.57 × 1012) / (8.44 × 10-4)
