Exponents • Topic 4 of 4

Scientific Notation

Scientific notation writes a number as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer. A positive n shifts the decimal right (large numbers); a negative n shifts it left (small numbers). So 4,500 = 4.5 × 10³ and 0.0007 = 7 × 10⁻⁴. To multiply numbers in scientific notation, multiply the front parts and add the exponents; to divide, divide the fronts and subtract exponents, then adjust so the front stays between 1 and 10. Scientific notation appears in SAT science-context and very-large/very-small number problems.

✅ Solved examples

1. Write 32,000 in scientific notation.
Move the decimal 4 places: 3.2 × 10⁴.
2. Write 0.0045 in scientific notation.
Move the decimal 3 places right: 4.5 × 10⁻³.
3. Write 6.1 × 10³ as a normal number.
Shift the decimal 3 right: 6,100.
4. Multiply (2 × 10³)(3 × 10⁴).
Multiply fronts (6) and add exponents (7): 6 × 10⁷.

✏️ Practice — try these, take hints as needed

1. Write 540,000 in scientific notation.
Front between 1 and 10: 5.4.
Count decimal places moved.
× 10^?
5.4 × 10⁵.
2. Write 0.00072 in scientific notation.
Front 7.2.
Small number → negative exponent.
Count places.
7.2 × 10⁻⁴.
3. Write 8.3 × 10² as a normal number.
Shift the decimal 2 right.
8.3 → 830.
—
830.
4. Multiply (4 × 10²)(2 × 10⁵).
Multiply fronts: 8.
Add exponents: 7.
—
8 × 10⁷.
5. Divide (6 × 10⁸)/(3 × 10²).
Divide fronts: 2.
Subtract exponents: 6.
—
2 × 10⁶.

📝 Topic test — 8 questions

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