Converters & Notation · Grades 7–10
Scientific Notation: How to Write and Convert Numbers
Why use it
Numbers like the distance to a star or the size of a virus have many zeros. Scientific notation keeps the digits that matter and puts the scale in the exponent.
Large numbers: move the point left
For 52,000 move the decimal point four places left to get 5.2, so the exponent is +4: 5.2 × 10⁴.
52,000
- Decimal: 52000
- E-notation: 5.2e4
Step-by-step working 3 steps
- 1Standard form needs 1 ≤ |a| < 10
Write the number as a × 10ⁿ where a has exactly one non-zero digit before the point.
- 2Move the decimal point
52000 → 5.2
The point moves 4 places left, so the exponent is +4.
- 3Write the result
52000 = 5.2 × 10⁴
Small numbers: move the point right
For 0.00047 move it four places right: 4.7 × 10⁻⁴. Small numbers get negative exponents.
0.00047
- Decimal: 0.00047
- E-notation: 4.7e-4
Step-by-step working 3 steps
- 1Standard form needs 1 ≤ |a| < 10
Write the number as a × 10ⁿ where a has exactly one non-zero digit before the point.
- 2Move the decimal point
0.00047 → 4.7
The point moves 4 places right, so the exponent is −4.
- 3Write the result
0.00047 = 4.7 × 10⁻⁴
Reading E-notation
Calculators and spreadsheets write 3.2 × 10⁵ as 3.2e5. The “e” means “times ten to the power of”.
Common mistakes
Leaving a out of range
12 × 10³ should be 1.2 × 10⁴.
Wrong exponent sign
Numbers below 1 have negative exponents.
Adding exponents when adding
Exponents add when multiplying, not when adding.
Frequently asked questions
How do I multiply numbers in scientific notation?
Multiply the a parts and add the exponents, then renormalise if needed.
