Standard form · Year 11

In Year 11 you learn: standard form in real problems.

Standard form (scientific notation) writes very large and very small numbers as a number from 1 to 10 multiplied by a power of 10, like 3 × 10^8 m/s for the speed of light. It makes such numbers easy to read, compare and calculate with.

Key facts

• Standard form is A × 10^n where 1 ≤ A < 10 and n is a whole number.
• Large numbers have a positive power: 45,000 = 4.5 × 10^4.
• Small numbers have a negative power: 0.00032 = 3.2 × 10^(−4).
• Compare: the bigger power of 10 wins; if the powers match, compare A.
• Multiply: multiply the A parts and add the powers. Divide: divide and subtract.
• Add or subtract: change to ordinary numbers (or the same power) first.
• Tidy up if A ends up 10 or more: 24 × 10^5 = 2.4 × 10^6.

Worked examples

Other years

• Standard form · Year 9
• Standard form · Year 10