Standard Form Calculator
Convert any number to standard form (scientific notation). Standard form expresses numbers as a coefficient between 1 and 10 multiplied by a power of 10. This notation is used in science, engineering, and mathematics to handle very large or very small numbers efficiently.
What is Standard Form?
Standard form (also called scientific notation) writes numbers as: a × 10ⁿ where 1 ≤ |a| < 10 and n is an integer. For example, 45,600,000 becomes 4.56 × 10⁷.
How to Convert to Standard Form
- Move the decimal point until you have a number between 1 and 10
- Count how many places you moved the decimal
- If you moved left, the exponent is positive. If right, it is negative
- Write as: coefficient × 10^(number of places moved)
Standard Form Examples
| Number | Standard Form |
|---|---|
| 0.00045 | 4.5 × 10⁻⁴ |
| 0.0072 | 7.2 × 10⁻³ |
| 1 | 1 × 10⁰ |
| 350 | 3.5 × 10² |
| 5000 | 5 × 10³ |
| 72000 | 7.2 × 10⁴ |
| 1000000 | 1 × 10⁶ |
| 299792458 | 2.998 × 10⁸ |
| 6022000000000000000000000 | 6.022 × 10²³ |
Frequently Asked Questions
What is the difference between standard form and scientific notation?
They are the same thing. "Standard form" is the term used in the UK and many countries, while "scientific notation" is more common in the US. Both express numbers as a × 10ⁿ.
How do I write 0.00045 in standard form?
Move the decimal 4 places to the right to get 4.5. Since you moved right, the exponent is negative: 4.5 × 10⁻⁴.
What is 10⁰?
10⁰ = 1. Any number raised to the power of zero equals 1. So a number in standard form with exponent 0 is just the coefficient itself (between 1 and 10).
When is standard form used?
Standard form is used in science (speed of light = 3 × 10⁸ m/s), chemistry (Avogadro's number = 6.022 × 10²³), astronomy (distances in light years), and computing (floating-point numbers).