Standard form

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Standard form

In standard form, a number is always written as: A × 10 n. A is always between 1 and 10. n tells us how many places to move the decimal point.

Write 15 000 000 in standard index form.

15 000 000 = 1.5 × 10 000 000

= 1. 5 × 10 to the power of 7

Standard form can be applied to decimals as well

0.000467 = 4.67 × 0.0001

= 4.67 × 10 to the power of -4

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Adding and subtracting

Convert them into ordinary numbers, do the calculation, then change them back if you want the answer in standard form.

4.5 × 10 to the power of 4 + 6.45 × 10 to the power of 5

= 45,000 + 645,000 = 690,000

= 6.9 × 10 to the power of 5

Multiplying and dividing

To multiply powers you add them

10 to the power of 5 × 10 to the power of 3

= 10 to the power of 8

To divide powers you subtract them

10 to the power of 5 ÷ 10 to the power of 3

= 10 to the power of 2