Scientific notation
Write huge and tiny numbers without getting dizzy
What is this about?
Scientific notation is a compact way to write very large or very small numbers: a number between 1 and 10 multiplied by a power of 10. The distance from Earth to the Sun (150,000,000 km) becomes 1.5 × 10⁸. The exponent tells you how many places the decimal point moves: positive for large numbers, negative for small ones.
The rule to remember
Place the decimal point right after the first non-zero digit and count how many places you moved it: that's the exponent. If the original number was greater than 10, the exponent is positive; if it was less than 1, it's negative.
Example 1
Write 340,000 in scientific notation
- 1Place the point after the first digit: 3.4.
- 2Count how many places the point moved from the end: 3 4 0 0 0 0 → 5 places.
- 3The original number is large (greater than 10), so the exponent is positive.
- 4Result: 3.4 × 10⁵.
Result: 3.4 × 10⁵
Example 2
Write 0.00072 in scientific notation
- 1The first non-zero digit is the 7: the point goes right after it → 7.2.
- 2Count the places the point moves to the right: 0.00072 → 4 places.
- 3The original number is less than 1, so the exponent is negative.
- 4Result: 7.2 × 10⁻⁴.
Result: 7.2 × 10⁻⁴
The most common mistake
Many people write
45,000 = 45 × 10³
Why it's wrong
The first factor must be between 1 and 10, and 45 is not. Move the point one more place: 4.5 × 10⁴. Check: 4.5 × 10,000 = 45,000. ✓
Did it click?
The best way to find out is to try. These exercises are exactly on this topic.
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