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Scientific notation

Q: How do I write 0.00045 in scientific notation?

Move the decimal point four places to the right to get 4.5, so the answer is 4.5 × 10 to the power minus 4.

Q: Why not just write the full number?

Long strings of zeros are easy to miscount, and scientific notation makes the number of significant figures clearer.

Q: How do I multiply numbers in scientific notation?

Multiply the decimal parts and add the powers of ten. For example, (3 × 10⁴)(2 × 10⁵) = 6 × 10⁹.

Beginner

Writing numbers as a×10ⁿ to handle very large or small values.

Key relationa × 10ⁿ

Scientific notation writes a number as a × 10ⁿ with 1 ≤ a < 10. It makes huge and tiny values easy to compare (just look at the exponent) and to multiply: add the exponents, multiply the leading numbers.

Worked example

(3×10⁸)×(2×10⁻³) = 6×10⁵. Dividing 6×10⁵ by 2×10² gives 3×10³.

Common mistake

When adding numbers, first give them the same exponent. 2×10³ + 5×10² is 2.5×10³, not 7×10⁵.

In more detail

Scientific notation writes a number as a coefficient between 1 and 10 times a power of ten. It makes calculations with very large or very small values easier to follow and to check.

Real-world uses

The distance to a nearby star, about 4 × 10 to the power 16 metres, is easier to read in this form.
Calculators display small and large results in scientific notation automatically.
Astronomers write the Sun's mass as 2 × 10³⁰ kg, which is far easier to read and compare than 2 000 000 000 000 000 000 000 000 000 000 kg.

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Frequently asked questions

How do I write 0.00045 in scientific notation?