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Standard form
Scientists write huge and tiny numbers in standard form, like the mass of the Earth or the size of an atom.
What it looks like
A × 10n, where A is at least 1 and less than 10, and n is a whole number.
4 500 000 = 4.5 × 106
0.00032 = 3.2 × 10-4
4 500 000 = 4.5 × 106
0.00032 = 3.2 × 10-4
Converting
Count how many places the digits move.
Big numbers: positive power. Small numbers (less than 1): negative power.
7.1 × 103 = 7100
6 × 10-2 = 0.06
Big numbers: positive power. Small numbers (less than 1): negative power.
7.1 × 103 = 7100
6 × 10-2 = 0.06
Calculating
Multiply: multiply the numbers, add the powers.
(2 × 103) × (4 × 105) = 8 × 108
If the front number goes past 10, adjust: 15 × 104 = 1.5 × 105
(2 × 103) × (4 × 105) = 8 × 108
If the front number goes past 10, adjust: 15 × 104 = 1.5 × 105
Work out (3 × 104) × (5 × 106). Give your answer in standard form.
- 3 × 5 = 15
- 104 × 106 = 1010
- 15 × 1010 = 1.5 × 1011
Answer: 1.5 × 1011
A × 10n with 1 ≤ A < 10. Big numbers have positive powers, small numbers negative. Multiply the numbers and add the powers, then adjust so A is less than 10.
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