Quick answer: Scientific notation writes very large or small numbers as a coefficient between 1 and 10 times a power of ten: 6,500,000 becomes 6.5 times 10 to the 6th. Multiply by adding exponents and divide by subtracting them. E-notation means the same thing, so 3.2E8 is 3.2 times 10 to the 8th.
Last reviewed: October 2026
Key facts
- 4,500,000 = 4.5 × 106; 0.00000052 = 5.2 × 10−7.
- Standard form keeps one non-zero digit before the point: 1 ≤ coefficient < 10.
- The speed of light is about 3 × 108 m/s; a hydrogen atom ≈ 1 × 10−10 m.
- On calculators it often appears as E notation: 4.5E6.
Astronomy and microbiology share a problem: numbers too big or too small to write out. Scientific notation (standard form) compresses them into a coefficient times a power of ten — and this free converter switches between that form and ordinary numbers both ways.
Enter an ordinary number to see its standard form, or enter standard form to expand it. It is the fastest way to read and write the huge and tiny numbers of science.
How to use
- Enter an ordinary number (e.g. 4500000) or standard form (e.g. 4.5×10^6).
- The converter detects the direction automatically.
- Read the converted value with the power of ten shown.
- Use the result in homework, lab reports or further calculations.
Standard form rules
| Term | Meaning |
|---|---|
| a | The coefficient — one non-zero digit before the decimal point. |
| n | The exponent — how many places the point moved (negative for tiny numbers). |
Move the decimal point until one digit remains before it; the number of moves (with sign) is the exponent.
Worked examples
Big number
4,500,000 → standard form: move the point 6 places left → 4.5 × 106.
3.6 × 109 → ordinary: move the point 9 right → 3,600,000,000.
Tiny number
0.00000052 → standard form: move the point 7 places right → 5.2 × 10−7.
Negative exponents mean “divide by”: 10−7 = 1/10,000,000.
Powers of ten you meet everywhere
| Power | Name | Example |
|---|---|---|
| 1012 | Tera (T) | Hard drive sizes (TB) |
| 109 | Giga (G) | Processor speeds (GHz) |
| 106 | Mega (M) | Camera megapixels |
| 103 | Kilo (k) | Kilometres, kilograms |
| 100 | One | Ordinary numbers |
| 10−3 | Milli (m) | Millimetres, milligrams |
| 10−6 | Micro (µ) | Micrometres, bacteria |
| 10−9 | Nano (n) | Nanometres, atoms |
Frequently asked questions
Why use scientific notation?
It keeps huge and tiny numbers readable and makes their scale obvious: 3 × 108 instantly says “hundreds of millions”.
What is E notation?
Calculator shorthand: 4.5E6 means 4.5 × 106. The E stands for “exponent of ten”.
What does a negative exponent mean?
Division by that power of ten: 10−3 = 1/1,000 = 0.001.
How do I add numbers in scientific notation?
Convert to the same exponent first, add the coefficients, then re-normalise: 2×106 + 3×105 = 2.3×106.
Is “standard form” the same thing?
Yes — UK schools say “standard form”, US schools say “scientific notation”. Same mathematics.
How do I type scientific notation on a Casio calculator?
Use the EXP button (sometimes labelled EE or ×10^x): to enter 3.5 × 10−6 press 3.5, EXP, (−), 6. To make answers display in scientific form, switch the display mode to SCI (or ENG for engineering notation) via the MODE or SETUP menu. Do NOT use the ^ hat key for entry — the calculator treats that as two separate numbers and order of operations breaks.
What is engineering notation?
A cousin of scientific notation where the exponent is always a multiple of 3, so it lines up with SI prefixes: 45,000 = 45 × 103 (kilo), 4,500,000 = 4.5 × 106 (mega). The rule is the same, only the coefficient is allowed to be between 1 and 999 instead of 1 and 10.
Sources
- Khan Academy — Scientific notation lessons
- Maths is Fun — Scientific notation with examples
Key takeaways
- N = a × 10n with 1 ≤ a < 10 — one digit before the point.
- Positive exponents = big; negative = tiny (10−3 = 0.001).
- E notation (4.5E6) is the same thing in calculator shorthand.
Comments
Leave a comment