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Very large numbers! BOOM! How far? 92 000 000 miles Very large numbers! Happy 70th Birthday! SPLAT! Howyears many= seconds in 70 years? 70 2 200 000 000 seconds! Very large numbers! Dinosaurs roamed the earth 228 million years ago Standard Form When writing a number in standard form / scientific notation it must be in the form : n a x 10 Where ‘a’ MUST be greater than 1 and less than 10 3 i.e 4.2 x 10 A short cut 8 000 000 Step 1: Put a decimal point at the end of the number 8 000 000. Step 2:Move the decimal point to get a number between 1 and 10 8. 000 000. Step 3: Write the number in standard form / scientific notation 8 000 000 8 10 Between 1 and 10 6 The point moved 6 places A short cut 92 000 000 Step 1: Put a decimal point at the end of the number 92 000 000. Step 2:Move the decimal point to get a number between 1 and 10 92 . 000 000. Step 3: Write the number in standard form / scientific notation 92 000 000 9.2 10 Between 1 and 10 7 The point moved 7 places A short cut 228 000 000 Step 1: Put a decimal point at the end of the number 228 000 000. Step 2:Move the decimal point to get a number between 1 and 10 . 000 000. 228 Step 3: Write the number in standard form / scientific notation 228 000 000 2.28 10 8 Between 1 and 10 The point moved 8 places Standard Form (1) 30 000 3 1045 (2) 700 000 7 10 3 (3) 5 300 5.3 10 5 (4) 470 000 4.7 106 (5) 9 500 000 9.5 107 (6) 18 300 000 1.83 10 5 (7) 329 000 3.29 10 6 (8) 2 560 000 2.56 10 (9) 12 000 000 000 1.2 1010 6 (10) 9 990 000 9.99 10 Changing back The point moves 7 places 8.6 10 8.60000000 . =86 000 000 7 Hint: Add 7 zeros, although you probably won’t need them all. Zeros after the point aren’t needed. Changing back The point moves 5 places 3.46 10 3.4600000 . =346 000 5 Hint: Add 5 zeros, although you probably won’t need them all. Zeros after the point aren’t needed. Changing back (1) 6 105 (2) 8 103 (3) 6.5 105 (4) 1.2 108 (5) 3.71106 (6) 3.3 104 (7) 7.91106 (8) 5.55 107 (9) 1.05 104 (10) 3.033 109 = 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 Very small numbers! How wide is an atom? 0.000 000 000 1 metres wide! Standard Form for small numbers Move the point to get a number between 1 and 10 0.000 000 000 1 . 110 10 The point moved 10 places. Negative sign for small numbers. 1 10-10metres wide Standard Form for small numbers Move the point to get a number between 1 and 10 . 7.6 10 0.000 000 76 7 The point moved 7 places. Negative sign for small numbers. Standard Form for small numbers Move the point to get a number between 1 and 10 0.000 001. 93 1.93 10 6 The point moved 6 places. Negative sign for small numbers. Standard Form for small numbers 4 (1) 0. 000 3 3 10 5 (2) 0.000 07 7 10 4 (3) 0.000 45 4.5 103 (4) 0.003 4 3.4 10 (5) 0. 000 724 7.24 104 7 (6) 0.000 000 494 4.94 10 5 (7) 0.000 095 9.5 108 (8) 0.000 000 098 9.8 10 4 (9) 0.000 1 03 1.03 1010 (10) 0.000 000 000 66 6.6 10 Changing back small numbers -3 so remember to move point left for small numbers. Hint: Add 3 zeros to the left of the number. . 2. 2 10 000 -3 = 0.002 Changing back small numbers -5 so remember to move point left for small numbers. Hint: Add 5 zeros to the left of the number. 8.6 . 8.6 10 00000 -5 = 0.000 086 Changing back small numbers Hint: -6 so remember to move point left for Add 6 zeros to the left of the number. small numbers. 5.16 5.16 10 000000 . -6 = 0.000 00516 Changing back small numbers (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 4 = 0.000 5 9 105 = 0.000 09 3 5.8 10 = 0.005 8 7 6.2 10 = 0.000 000 62 6.45 106 = 0.000 006 45 5.3 107 = 0.000 000 53 6 = 0.000 009 17 9.17 103 2.12 10 = 0.002 12 5 2.03 10 = 0.000 020 3 9 6.032 10 = 0.000 000 006 032 5 10