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www.mathsrevision.com I. SCIENTIFIC NOTATION A METHOD OF DEALING WITH VERY LARGE AND VERY SMALL NUMBERS IN SCIENCE

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Very large numbers! BOOM! How far? 92 000 000 miles

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Very small numbers! How wide is an atom? 0.000 000 000 1 metres wide!

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Made up of three parts: the coefficient, the base and the exponent. A. Writing Numbers in Scientific Notation 5.67 x 10 5 coefficient base exponent

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1. The coefficient must be between 1 and 9.9999999999999999999999999999999 2. The base must be 10 3. The exponent shows how many places the decimal moved. 5.67 x 10 5 coefficient base exponent B. Scientific Notation Rules:

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Examples of Scientific Notation 363,000,000,000 = 3.63 x 10 11 0.00035 = 3.5 x 10 -4

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Numbers larger than 1, the exponent is positive Example: 8.38 x 10 5 = 838,000 Numbers less than 1, the exponent is negative Example: 5.03 x 10 -3 = 0.00503 C. Scientific Notation Exponents

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92 000 000.. Add the decimal point Between 1 and 10 The point moved 7 places Move the point to get a number between 1 and 10 D. Scientific Notation for Large Numbers

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0.000 000 000 1. The point moved 10 places. Negative sign for small numbers. Move the point to get a number between 1 and 10 E. Scientific Notation for Small Numbers

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Examples of Scientific Notation 363,000,000,000 = 3.63 x 10 11 0.00035 = 3.5 x 10 -4

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a.700 m c. 0.0054 kg b.38 000 m d. 0.000 006 87 kg Practice – Convert to Scientific Notation 7 x 10 2 m 3.8 x 10 4 m 5.4 x 10 -3 kg 6.87 x 10 -6 kg

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=86 000 000 Zeros after the point aren’t needed. The point moves 7 places to the right 8.6 0000000. Hint: Add 7 zeros, although you probably won’t need them all. F. Changing back large numbers

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G.Changing back small numbers = 0.000 00516 5.16 000000. Hint: Add 6 zeros to the left of the number. -6 so remember to move point left for small numbers.

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a.1.26 x 10 4 kg c. 9.02 x 10 3 kg b.5.36 x 10 -2 m d. 7.6 x 10 -5 m Practice – Convert back to a number 12600 kg 0.0536 m 9020 kg 0.000076 m

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H. Multiplying using Scientific Notation To multiply numbers in scientific notation, multiply the coefficients then add the exponents To multiply numbers in scientific notation, multiply the coefficients then add the exponents Move the decimal point so that the number is in scientific notation Move the decimal point so that the number is in scientific notation

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www.mathsrevision.com Examples: Multiplying in Scientific Notation

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I. Dividing using Scientific Notation To divide numbers written in scientific notation: To divide numbers written in scientific notation: –divide the coefficients then –subtract the exponent in the denominator (bottom) from the exponent in the numerator (top) => “top – bottom” or “first – second” Express the final answer in scientific notation Express the final answer in scientific notation

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www.mathsrevision.com Example: Dividing Numbers in Scientific Notation

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If you have to move the decimal to the LEFT, Add to the exponent 1.26 x 10 4 12.6 x 10 3 = 1.26 x 10 4 If you have to move the decimal to the RIGHT, Subtract from the exponent x 10 3 0.902 x 10 4 = 9.02 x 10 3 Hint for converting an answer to scientific notation LARS: Left Add, Right Subtract

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Practice – Multiplying and Dividing 1.2 x 10 11 3 x 10 1 2 x 10 -1 1.2 x 10 -1

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