Work out (4.5 × 106) ÷ (9 × 10−2), giving the answer in standard form.
- Divide the number parts: 4.5 ÷ 9 = 0.5.
- Subtract the indices: 6 − (−2) = 8, giving 0.5 × 108.
- Adjust: 0.5 = 5 × 10−1, so 0.5 × 108 = 5 × 107.
Answer: 5 × 107
Standard form
Maths · Number. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
Standard form is a way to write very large and very small numbers. The number is written as A × 10n, where A is at least 1 and less than 10, and n is an integer.
The index n tells you how many places the digits move. A positive n means a large number: 3.2 × 104 = 32 000. A negative n means a number smaller than 1: 3.2 × 10−4 = 0.000 32.
To calculate in standard form, deal with the number parts and the powers of ten separately, using the rules of indices. If the number part of your answer is not between 1 and 10, adjust it at the end.
Rules to remember
- Standard form is A × 10n with 1 ≤ A < 10 and n an integer.
- Large number: n is positive. Number less than 1: n is negative.
- Multiply: multiply the A values and add the indices.
- Divide: divide the A values and subtract the indices.
- Add or subtract: make the powers of ten the same first, or change to ordinary numbers.
- Adjusting: 24 × 103 = 2.4 × 104 and 0.5 × 108 = 5 × 107.
- (A × 10n)2 = A2 × 102n
Common mistake
Leaving an answer such as 24 × 103. It has the right value but is not standard form, because 24 is not less than 10. Write 2.4 × 104.
Worked example
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