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Standard form

Standard form writes a number as a number from 1 up to but not including 10, times a power of ten. The decimal point is moved so that one digit stands in front, and the number of places becomes the exponent. Positive exponents give large numbers, negative ones give small numbers. When you divide two numbers in standard form, you divide the coefficients and subtract the exponents. The travel time of light below is exactly 500 seconds, and the minutes are that time divided by 60.

k⋅10nk \cdot 10^n1 ≤ k < 10
a⋅10mb⋅10n=ab⋅10m−n\frac{a \cdot 10^m}{b \cdot 10^n} = \frac{a}{b} \cdot 10^{m-n}division

Symbols

kkthe coefficient
nnthe exponent

Example

45 000=4.5⋅10445\,000 = 4.5 \cdot 10^4.

The distance to the Sun 1.5⋅1081.5 \cdot 10^8 km and the speed of light 3⋅1053 \cdot 10^5 km/s give 1.5⋅1083⋅105=500\dfrac{1.5 \cdot 10^8}{3 \cdot 10^5} = 500 seconds, which is 50060≈8.33\dfrac{500}{60} \approx 8.33 minutes.

One digit before the decimal point. The course says just over 8 minutes for the same journey.
Practise powers and standard form for free →

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Part of Mathematics 2P: Powers and standard form.