Problems Involving Exponents
7-10Scientific Notation
Overview
A number is in scientific notation when written as a × 10^n, with 1 ≤ a < 10.
Key ideas
- Move the decimal so the first factor is between 1 and 10.
- Count places moved → exponent (left positive, right negative).
- Useful for very large and very small numbers.
Worked examples
Example 1
Problem. Write 53,000 in scientific notation.
Solution. 5.3 × 10^4
Example 2
Problem. Write 0.0042 in scientific notation.
Solution. 4.2 × 10^(−3)
Practice
Try each one. Click Show answer when ready.
- 1.
Write 670,000.
- 2.
Write 0.00091.
- 3.
Compute (2 × 10^3)(3 × 10^4).
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Express 0.0000045 in scientific notation.
- 2.
Compute: (3 × 10⁵)(2 × 10⁻³) ÷ (6 × 10²).