Scientific Notation (Standard Form) Explained

Scientific notation writes a number as $a \times 10^n$, where $1 \le |a| < 10$ and $n$ is a whole number. Large numbers have a positive power and small numbers a negative one. To convert, move the decimal point until one non-zero digit is in front of it and count how many places it moved.

Large numbers

$602\,000\,000$: move the point 8 places left to get $6.02$, so

Small numbers

$0.000045$: move the point 5 places right to get $4.5$, so

Converting back

$3.1 \times 10^5 = 310\,000$ (move the point 5 places right). $7.1 \times 10^{-3} = 0.0071$ (move it 3 places left).

Multiplying and dividing

Multiply the front numbers and add the powers:

Divide the front numbers and subtract the powers:

If the front number ends up outside 1–10, adjust: $12 \times 10^5 = 1.2 \times 10^6$.

Engineering notation

Engineering notation uses powers that are multiples of 3, matching prefixes like kilo ($10^3$), mega ($10^6$) and micro ($10^{-6}$). For example, $45 \times 10^{-6}$.

Common mistakes

• Writing $45 \times 10^{-6}$ and calling it scientific notation (the front must be under 10).
• Getting the sign of the power the wrong way round.
• Forgetting to adjust after multiplying.

Practice questions

1. Write $93\,000\,000$ in scientific notation.
2. Write $0.00062$ in scientific notation.
3. Calculate $(4 \times 10^3)(3 \times 10^{-5})$.

Answers: 1) $9.3 \times 10^7$ 2) $6.2 \times 10^{-4}$ 3) $1.2 \times 10^{-1}$

Convert any number with the scientific notation calculator, round results with the rounding calculator, and read rounding and significant figures.

Frequently asked questions

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