Maths: Applications and Interpretation · Number and algebra. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
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Standard form writes any number as a × 10k, where a is at least 1 but less than 10 and k is an integer. Large numbers have a positive k and small numbers have a negative k. To multiply or divide, work with the a parts and the powers of 10 separately, then adjust so that a is back between 1 and 10.
A rounded value hides a range of possible true values. The lower and upper bounds are half a rounding unit below and above the stated value.
Percentage error compares an approximate value with the exact one. It is always measured against the exact value and is never negative.
Students divide by the approximate value in the percentage error formula. The exact value always goes in the denominator. Also check that your final a is between 1 and 10: 0.7 × 1010 is not standard form.
Answer: 7 × 109
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