Algebra I Recipe: Scientific Notation

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.

Examples:

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.

Examples:

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.

Examples:

(1.27 × 10^-6)(9.35 × 10²)

(8.31 × 10¹⁴)(7.16 ×10^-5)

(2.13 × 10^-7) / (9.26 × 10³)

(3.57 × 10¹²) / (8.44 × 10^-4)