Standard form

Description

Standard form (scientific notation) is a way of writing very large or very small numbers concisely.

$$a \times 10^n \quad \text{where } 1 \leq a < 10 \text{ and } n \text{ is an integer}$$

Large numbers: $3,400,000 = 3.4 \times 10^6$ Small numbers: $0.000052 = 5.2 \times 10^{-5}$

Multiplying in standard form: $$(3 \times 10^4) \times (2 \times 10^3) = 6 \times 10^7$$

Adding/subtracting: convert to the same power of 10 first, or convert back to ordinary numbers.

$$(3.5 \times 10^5) + (2 \times 10^4) = 35 \times 10^4 + 2 \times 10^4 = 37 \times 10^4 = 3.7 \times 10^5$$

The result must always be back in standard form ($1 \leq a < 10$).

Common error: writing $13.4 \times 10^5$ — the digit part must be between 1 and 10. Adjust: $13.4 \times 10^5 = 1.34 \times 10^6$.

Links

Indices Basic indices

Use the $\times 10^x$ key to enter standard form directly. The ENG button converts to engineering notation.