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www.mathsrevision.com Scientific Notation www.mathsrevision.com Standard form / Scientific Notation Scientific Notation very small numbers Scientific Notation to Number Form MTH 4-06b

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www.mathsrevision.com Starter Questions www.mathsrevision.com X MTH 4-06b

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www.mathsrevision.com Learning Intention Success Criteria 1.To understand and use the quick method to put large numbers into scientific notation. 1.To show a very quick way of putting a large number in scientific notation very quickly. Scientific Notation MTH 4-06b

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Very large numbers! BOOM! How far? 92 000 000 miles www.mathsrevision.com MTH 4-06b

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How many seconds in 70 years? 70 years = 2 200 000 000 seconds! Very large numbers! Happy 70 th Birthday! SPLAT! www.mathsrevision.com MTH 4-06b

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Dinosaurs roamed the earth 228 million years ago Very large numbers! www.mathsrevision.com

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Short hand ! 100 = 10 x 10 1 000 = 10 x 10 x 10 100 000 = 10 x 10 x 10 x 10 x 10 10 000 = 10 x 10 x 10 x 10 1 000 000 = 10 x 10 x 10 x 10 x 10 x 10 10 www.mathsrevision.com MTH 4-06b = 10 1 = 10 2 = 10 3 = 10 4 = 10 5 = 10 6

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Standard Form 200 = 2 x 100 4 000 = 4 x 1000 500 000 = 5 x 100 000 70 000 = 7 x 10 000 3 000 000 = 3 x 1 000 000 This is also known as Scientific Notation. www.mathsrevision.com MTH 4-06b = 2 x 10 2 = 4 x 10 3 = 7 x 10 4 = 5 x 10 5 = 3 x 10 6 Scale of BIG Numbers

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Standard Form Exercise 1 www.mathsrevision.com (1)2 000 (2) 20 000 (3) 500 (4) 800 000 (5) 9 000 000 = 5 x 100 = 8 x 100 000 = 2 x 10 000 = 9 x 1 000 000 = 2 x 1000 MTH 4-06b = 2 x 10 3 = 2 x 10 4 = 5 x 10 2 = 8 x 10 5 = 9 x 10 6

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Add the decimal point A short cut 8 000 000.. Between 1 and 10 The point moved 6 places Move the point to get a number between 1 and 10 www.mathsrevision.com MTH 4-06b = 8 x 10 6

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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 www.mathsrevision.com A short cut MTH 4-06b = 9.2 x 10 7 9.2 x 10 7 miles

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2 200 000 000.. Add the decimal point Between 1 and 10 The point moved 9 places Move the point to get a number between 1 and 10 Happy Birthday: Seconds old! A short cut MTH 4-06b = 2.2 x 10 9 = 2.2 x 10 9

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228 000 000.. Add the decimal point Between 1 and 10 The point moved 8 places Move the point to get a number between 1 and 10 www.mathsrevision.com A short cut MTH 4-06b = 2.28 x 10 8 = 2.28 x 10 8 years old

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www.mathsrevision.com Standard Form (1) 30 000 (2) 700 000 (3) 5 300 (4) 470 000 (5) 9 500 000 (6) 18 300 000 (7) 329 000 (8) 2 560 000 (9) 12 000 000 000 (10) 9 990 000 MTH 4-06b = 3 x 10 4 = 7 x 10 5 = 5.3 x 10 3 = 4.7 x 10 5 = 9.5 x 10 6 = 18.3 x 10 7 = 3.29 x 10 5 = 2.56 x 10 6 = 1.2 x 10 10 = 9.99 x 10 6

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www.mathsrevision.com Starter Questions www.mathsrevision.com MTH 4-06b

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www.mathsrevision.com Scientific Notation www.mathsrevision.com Learning Intention Success Criteria 1.Know how to expand large numbers in scientific notation to number format. 1.To understand how to change large numbers from Scientific Notation to number form. MTH 4-06b

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=86 000 000 Zeros after the point aren’t needed. The point moves 7 places 8.6 0000000. Hint: Add 7 zeros, although you probably won’t need them all. www.mathsrevision.com Changing back MTH 4-06b 8.6 x 10 7 =

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www.mathsrevision.com =346 000 Zeros after the point aren’t needed. The point moves 5 places 3.46 00000. Hint: Add 5 zeros, although you probably won’t need them all. Changing back MTH 4-06b 3.46 x 10 5 =

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www.mathsrevision.com Changing back (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) = 600 000 = 8 000 = 650 000 = 120 000 000 = 3 710 000 = 33 000 = 7 910 000 = 55 500 000 = 10 500 = 3 033 000 000 MTH 4-06b

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Name that number! 10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 1 000 1 000 000 1 000 000 000 one thousand one million one billion one googol !!! www.mathsrevision.com MTH 4-06b = 1 x 10 3 = 1 x 10 6 = 1 x 10 9 = 1 x 10 100

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www.mathsrevision.com Starter Questions www.mathsrevision.com MTH 4-06b

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www.mathsrevision.com Scientific Notation www.mathsrevision.com Learning Intention Success Criteria 1.Know how to change very small numbers into scientific notation and how to do the reverse process. 1.To understand how to change very small numbers into Scientific Notation and vice versa. MTH 4-06b

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Very small numbers! How wide is an atom? 0.000 000 000 1 metres wide! www.mathsrevision.com MTH 4-06b

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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 www.mathsrevision.com Standard Form for small numbers MTH 4-06b = 1 x 10 -10 Scale of SMALL Numbers

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0.000 000 76. The point moved 7 places. Negative sign for small numbers. Move the point to get a number between 1 and 10 www.mathsrevision.com Standard Form for small numbers MTH 4-06b = 7.6 x 10 -7

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Standard Form for small numbers 0.000 001 93. The point moved 6 places. Negative sign for small numbers. Move the point to get a number between 1 and 10 www.mathsrevision.com MTH 4-06b = 1.93 x 10 -6

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Standard Form for small numbers www.mathsrevision.com (1) 0. 000 3 (2) 0.000 07 (3) 0.000 45 (4) 0.003 4 (5) 0. 000 724 (6) 0.000 000 494 (7) 0.000 095 (8) 0.000 000 098 (9) 0.000 1 03 (10) 0.000 000 000 66 MTH 4-06b

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= 0.002 2 000. Hint: Add 3 zeros to the left of the number. -3 so remember to move point left for small numbers.. www.mathsrevision.com Changing back small numbers MTH 4-06b 2 x 10 -3 =

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= 0.000086 8 6 00000. Hint: Add 5 zeros to the left of the number. -5 so remember to move point left for small numbers. www.mathsrevision.com Changing back small numbers MTH 4-06b 8.6 x 10 -5 =.

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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. www.mathsrevision.com MTH 4-06b 5.16 x 10 -6 =.

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www.mathsrevision.com (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) = 0.000 5 = 0.000 09 = 0.005 8 = 0.000 000 62 = 0.000 006 45 = 0.000 000 53 = 0.000 009 17 = 0.002 12 = 0.000 020 3 = 0.000 000 006 032 Changing back small numbers MTH 4-06b

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