Indices and standard form

# 1 2 8 1 9 81 d 1 10 10 000 1 express a as a power

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Unformatted text preview: t having any c2 fractions in your final answer. If a = b 3 and b = 3.4 Standard Form Standard form is a convenient way of writing very large or very small numbers. It is used on a scientific calculator when a number is too large or too small to be displayed on the screen. Before using standard form, we revise multiplying and dividing by powers of 10. Example 1 Calculate: (a) 3 × 10 4 (b) 3.27 × 10 3 (c) 3 ÷ 10 2 (d) 4.32 ÷ 10 4 Solution (a) 3 × 10 4 = 3 × 10 000 = 30 000 (b) 3.27 × 10 3 = 3.27 × 1000 = 3270 (c) 3 ÷ 10 2 = 3 100 = 0.03 49 MEP Y9 Practice Book A 3.4 (d) 4.32 ÷ 10 4 = = 4.32 10 000 432 1000 000 = 0.000432 These examples lead to the approach used for standard form, which is a reversal of the approach used in Example 1. In standard form, numbers are written as a × 10 n where 1 ≤ a < 10 and n is an integer. Example 2 Write the following numbers in standard form: (a) 5720 (b) 7.4 (c) 473 000 (d) 6 000 000 (e) 0.09 (f) 0.000621 Solution (a) 5720 = 5.72 × 1000 = 5.72 × 10 3 (b) 7.4 = 7.4 × 1 = 7.4 × 10 0 (c) 473 000 = 4.73 × 100 000 = 4.73 × 10 5 (d) 6 000 000 = 6 × 1000 000 = 6 × 10 6 (e) 0.09 = 9 100 = 9 ÷ 10 2 = 9 × 10 − 2 50 MEP Y9 Practice Book A (f) 0.000621 = = 6.21 10 000 6.21 10 4 = 6.21 × 10 − 4 Example 3 Calculate: (a) (3 × 10 ) × (4 × 10 ) (b) (6 × 10 ) ÷ (5 × 10 ) (c) (3 × 10 ) + (2 × 10 ) 6 7 4 3 −2 5 Solution (a) (3 × 10 ) × (4 × 10 ) 6 3 = (3 × 4) × (10 6 × 10 3 ) = 12 × 10 9 = 1.2 × 10 1 × 10 9 = 1.2 × 10 10 (b) (6 × 10 ) ÷ (5 × 10 ) 7 −2 = (6 ÷ 5) × (10 7 ÷ 10 − 2 ) = 1.2 × 10 9 (c) (3 × 10 ) + (2 × 10 ) 4 5 = 30 000 + 200 000 = 230 000 = 2.3 × 10 5 Note on Using Calculators Your calculator will have a key form. EE or EXP for entering numbers in standard For example, for 3.2 × 10 7 , press 3 . 2 51 EXP 7 MEP Y9 Practice Book A 3.4 which will appear on your display like this: 3.2 07 Some calculators also display the ' × 10 ' part of the number, but not all do. You need to find out what your calculator dis...
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