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Scientific Notation (Standard Form) The distance from the Earth to the Sun is 152,000,000 km. The nearest star to our Sun is 3800000000000000km (4 Light Years) away - Alpha Centauri. The mass of an atom is approximately 0.00000000000000000000000042 kg !! There must be an easier way of writing these! Indices are a really useful tool for writing very large and very small numbers in a simple way. (Remember Mathematicians are lazy!! They like to find simple, efficient ways of solving problems) Multiplying or dividing by 10 or multiples of ten is easy, all you have to do is move the decimal point. Eg: 2.45 x 10 = 24.5 3.78 x 100 = 378 58.5 ÷ 10 = 5.85 Try the following: 1. 67.25 X 10 = 3. 78.9 ÷ 10 = 2. 0.875 x 100 = 4. 34 x 10000 = Now remember from the worksheet you have just done that: 10 = 101 100 = 102 1000 = 103 etc Scientific Notation (Standard Form) is ‘standard’ because it is written the same way every time. This is a number with only one digit before the decimal point (but not zero) multiplied by a power of 10. Eg: 3.75 x 103 is the same as 3.75 x 1000 = 3750, so can you see the short cut? 4.657 X 105 = 4.657 x ______ = _________ SO, 7.3 x 10-2 = ________ Write a rule for converting a number in scientific form to a basic number. __________________________________________________ __________________________________________________ Try the puzzle sheet ‘Who is the Famous Fellow’ Now what if we want to convert a number to scientific form (it is just the opposite of what you have been doing! Eg: 349 = 3.49 X 102 Try the following: 24000 = 2.4 X 10_ 6730000 = ____ X 10_ 0.034 = 3.4 X 10_ Write each of the following using scientific notation: a 315 b 4300 c 6700 000 000 000 d 4.5 e 90 000 000 000 000 000 f 23 g 67 800 h 0.0122 i 0.007 89 j 0.234 56 k 0.000 78 l 0.000 005 m 61.78