What is scientific notation?
Scientific notation writes a number as a number from 1 up to (but not including) 10, times a power of ten: 4,000 is 4 × 10³ and 0.004 is 4 × 10⁻³. It makes very large and very small numbers short and easy to compare, which is why it's used so much in science.
Calculators and spreadsheets often show it as E notation, where E means “times 10 to the power”: 1.23E+10 is 1.23 × 10¹⁰.
Engineering notation uses powers of ten in steps of 3, like the metric prefixes: 37,000 is 37 × 10³ (kilo).
Source OpenStax Prealgebra 2e · 10.5 Integer Exponents and Scientific Notation ↗Microsoft Support · Display numbers in scientific notation ↗NIST · Metric (SI) prefixes ↗
How to convert to scientific notation
Here it is with your numbers:
- Move the decimal point so the first number is from 1 up to 10: 3.7.
- It moved 4 places to the left, so the power of ten is 4.
- Write it as a product with a power of ten: 3.7 × 10⁴.
- Check: 3.7 × 10⁴ written out is 37,000.
It means 37,000 is 3.7 × 10⁴, with the same 2 significant figures.
Only the significant digits go in the first number. The final zeros of a whole number like 37,000 don't count, so it is 3.7 × 10⁴; if they were measured, type a decimal point and zero (37,000.0) and they are kept: 3.70000 × 10⁴. See the Significant Figures Calculator for the counting rules.
Source NIST SP 1038 · significant digits (footnote 7) ↗
Scientific notation examples
| Number | Scientific notation |
|---|---|
| 48,000 | 4.8 × 10⁴ |
| 0.000125 | 1.25 × 10⁻⁴ |
| 0.000000084 | 8.4 × 10⁻⁸ |
| 91,200 | 9.12 × 10⁴ |
FAQs
How do I do scientific notation?
Move the decimal point until the number is at least 1 and less than 10, then multiply by 10 to the number of places you moved it. 37,000 is 3.7 × 10⁴; 0.0052 is 5.2 × 10⁻³.
Source OpenStax Prealgebra 2e · 10.5 Integer Exponents and Scientific Notation ↗
How do you multiply two scientific notations?
Multiply the first numbers and add the powers of ten. (3.1 × 10⁵) × (2.2 × 10⁷) is (3.1 × 2.2) × 10⁵⁺⁷, which is 6.82 × 10¹².
What is the sum of 5.3 × 10⁵ and 3.8 × 10⁴ in scientific notation?
5.68 × 10⁵. To add, write both with the same power of ten first: 3.8 × 10⁴ is 0.38 × 10⁵, and 5.3 + 0.38 is 5.68.
Source Common Core · Grade 8 Expressions & Equations (8.EE.A.4) ↗
Sources
- OpenStax Prealgebra 2e: 10.5 Integer Exponents and Scientific Notation
- Common Core: Grade 8 Expressions & Equations (8.EE.A.4)
- Microsoft Support: Display numbers in scientific notation
- NIST SP 1038: significant digits (footnote 7)
- NIST: Metric (SI) prefixes