Scientific notation chart
Scientific notation writes any number as a value between 1 and 10 multiplied by a power of ten. It is the standard way to handle very large or very small numbers compactly. This chart shows the powers of ten and how ordinary numbers map onto them.
Powers of ten
| Number | Scientific notation | Name |
|---|---|---|
| 1,000,000,000 | 1 × 10⁹ | billion |
| 1,000,000 | 1 × 10⁶ | million |
| 1,000 | 1 × 10³ | thousand |
| 100 | 1 × 10² | hundred |
| 10 | 1 × 10¹ | ten |
| 1 | 1 × 10⁰ | one |
| 0.1 | 1 × 10⁻¹ | tenth |
| 0.01 | 1 × 10⁻² | hundredth |
| 0.001 | 1 × 10⁻³ | thousandth |
| 0.000001 | 1 × 10⁻⁶ | millionth |
Examples
| Standard form | Scientific notation |
|---|---|
| 384,400 (km to the Moon) | 3.844 × 10⁵ |
| 299,792,458 (speed of light, m/s) | 2.998 × 10⁸ |
| 0.0000000001 (atom width, m) | 1 × 10⁻¹⁰ |
| 6,022 followed by 20 zeros | 6.022 × 10²³ |
| 0.00045 | 4.5 × 10⁻⁴ |
To write a number in scientific notation, move the decimal point until one nonzero digit remains in front of it, then the number of places you moved becomes the exponent. Moving left gives a positive exponent (large numbers); moving right gives a negative exponent (small numbers). The leading value, called the mantissa, stays between 1 and 10.
Need metric units or other conversions?
See the Metric Conversion Chart, or use the scientific calculator for arithmetic in this form.
How to convert to scientific notation
Place the decimal point after the first nonzero digit and count how many places it moved from its original spot. For 384,400 the decimal moves five places left, giving 3.844 times ten to the fifth. For a small number like 0.00045, the decimal moves four places right, giving 4.5 times ten to the negative fourth. The exponent records the move; its sign records the direction.
Why it is useful
Scientific notation keeps very large and very small numbers manageable and makes their scale obvious at a glance. Comparing ten to the twenty-third with ten to the eighth is far clearer than counting zeros. It also simplifies multiplication and division: multiply the leading numbers and add the exponents, a rule that powers most scientific and engineering arithmetic.
FAQ
How do you write a number in scientific notation?
Express it as a number between 1 and 10 times a power of ten. Move the decimal to leave one digit in front, and the number of places moved is the exponent.
What does a negative exponent mean?
It marks a number smaller than one. Ten to the negative third is 0.001, so a negative exponent means you divide by that power of ten.
What is 5,000 in scientific notation?
5 × 10³. The decimal moves three places left, giving an exponent of 3.