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Maths

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Standard index form

Adding and subtracting numbers in standard index form:

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

Example 1

4.5 × 104 + 6.45 × 105

= 45,000 + 645,000

= 690,000

= 6.9 × 105

Multiplying and dividing numbers in standard form:

Here you can use the rules for multiplying and dividing powers. Remember these rules:

  • To multiply powers you add, eg, 105 × 103 = 108
  • To divide powers you subtract, eg, 105 ÷ 103 = 102

Example 2

Simplify (2 × 103) × (3 × 106)

Solution

Multiply 2 by 3 and add the powers of 10:

(2 × 103) × (3 × 106) = 6 × 109

Question

Simplify (36 × 105) ÷ (6 × 103)

toggle answer

Answer

Did you get 6 ×102?

If not, remember that you should first work out 36 ÷ 6, then work subtract the powers of 10 (because it is division), like this:

(36 x 105) ÷ (6 × 103) = (36 ÷ 6) x (105 ÷ 103) = 6 ×102

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