Structure and calculation Revision Notes

Writing and interpreting standard form

Move the decimal point until the first number is between 1 and 10. Count the places moved: use a positive integer power for numbers at least 10 and a negative integer power for numbers between 0 and 1. For example, 0.00056 = 5.6 × 10^-4.

Calculating with powers of ten

For multiplication, multiply the coefficients and add the powers: (a × 10^m)(b × 10^n) = ab × 10^(m+n). For division, divide the coefficients and subtract the powers: (a × 10^m) ÷ (b × 10^n) = (a ÷ b) × 10^(m−n).

Adding and subtracting

Before adding or subtracting, rewrite the numbers with the same power of ten. Add or subtract the coefficients, then adjust the result so its coefficient is at least 1 but less than 10. Check the decimal position and size of the answer.