How to Use Standard Form in IGCSE Physics

Standard form (scientific notation) expresses numbers as $a \times 10^n$ where $1 \leq a < 10$.

Writing numbers in standard form

Move the decimal point until there is one non-zero digit before it. Count the number of places moved.

Multiplying in standard form

Multiply the coefficients and add the powers:

$(3 \times 10^4) \times (2 \times 10^3) = 6 \times 10^7$

If the coefficient becomes $\geq 10$, adjust:

$(5 \times 10^4) \times (4 \times 10^3) = 20 \times 10^7 = 2.0 \times 10^8$

Dividing in standard form

Divide the coefficients and subtract the powers:

$\frac{6 \times 10^8}{3 \times 10^5} = 2 \times 10^3$

Common IGCSE Physics values in standard form

Common errors and how to correct them

1. Wrong sign on the power. Large numbers have positive powers; small numbers have negative powers.
2. Calculator entry error. Do not multiply by 10 AND use the EXP button. Use only the EXP button.
3. Coefficient not between 1 and 10. If your answer is $45 \times 10^6$, rewrite as $4.5 \times 10^7$.

How to apply this in an exam

Give your final answer in standard form when the values are very large or small. Check the sign of the power. Round the coefficient to the appropriate number of significant figures.