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Standard Form A number expressed in standard form is a number written between 1 and 10 multiplied by 10 to an appropriate power. The use of standard form is to represent very small numbers or very large numbers For example 0.000 000 000 000 32 represented in standard form will be 214000 000 000 represented in standard form will be 3 . 2 10 2 . 14 10 11 13 Example Express each of the following in standard form (i) 0.000 000 462 (ii) 0.004 (iii) 90 000 (iv) 5910 000 000 Example Express each of the following as ordinary numbers (i) 1 . 6 10 8 (ii) 2 . 54 10 6 (iii) 7 10 12 (iv) 9 . 414 10 2 Example Write the following list in order of size starting with the smallest 1 . 5 10 8 8 . 7 10 1 , 27 000 000, 3 . 7 10 4 , 0.000 44, 3 . 2 10 7 Example The surface of the earth is about 509 970 000 km2. Express this in standard form correct to two significant figures. Example Without a calculator work out the following and give your answer in standard form. (a) 30 x 40 000 (b) 12 000 x 0.00005 (c) 1 . 1 10 6 10 (d) 5 . 4 10 9 10 (e) 0 . 00072 80000000 5 6 3 7 Example Work out the following (a) 360000 24000000 (b) 0 . 0004 20 000 000 Example 4 7 Given that A 6 10 and B 4 10 work out, without a calculator (i) AB (ii) A B Example 5 Given that X 1 . 2 10 and Y 5 10 9 work out , in standard form (i) (ii) XY X Y Here we use the button 1 . 2 – EXP And for Y we type 5 EXP for the standard form and type for X 5 EXP – 9 Example A rectangle has length AB = 1 . 3 10 km and width BC = 2 . 5 10 km. 5 Giving your answer in standard form, find a) the area, b) the perimeter of this rectangle. 4