LO To write and calculate numbers in standard

LO: To write and calculate numbers in standard form What is standard form? Standard Form is used a lot in maths and science as a convenient way of writing very large, or very small numbers for example: The distance from the earth to the sun is 149 000 km A hydrogen atom has a diameter of about 0. 000 2 mm

LO: To write and calculate numbers in standard form Large Numbers! Look at how these numbers have been broken down: 5000 = 5 × 102 = 5 × 1 000 = 5 × 103 50 000 = 5 × 10 000 you know how to write these as powers of 10 = 5 × 104

LO: To write and calculate numbers in standard form The rule! Standard form is: a number between 1 and 10 but not 0 1 g n i includ × positive a power of ten or nega tive E. g. 45, 000 can’t be written as 45 x 1000 = 45 x 103 It must be written as 4. 5 x 10, 000 = 4. 5 x 104

LO: To write and calculate numbers in standard form The trick! The number of decimal places you have moved it the number you put 10 to the power of!! 550 98, 000 = 5. 5 × 102 = 9. 8 × 104 7850000 = 7. 85 × 106 Moved the decimal in twice so 102 Moved the decimal four times so 104 Moved the decimal six times so 106

LO: To write and calculate numbers in standard form Now you try! Put these numbers into standard form: 6 000 = 6 × 103 4 000 = 4 × 103 400 = 4 × 102 450 = 4. 5 × 102 80 000 = 8 × 104 9 000 = 9 × 103 55000 3500 = 5. 5 × 104 4 00 000 = 4 × 105 750 000 = 7. 5 × 105 = 3. 5 × 103

LO: To write and calculate numbers in standard form Small Numbers! Look at how these numbers have been broken down: 0. 05 0. 005 = 5 × 0. 01 = 5 × 10 -2 = 5 × 0. 001 = 5 × 10 -3 0. 0005 = 5 × 0. 0001 = 5 × 10 -4 you know how to write these as negative powers of 10

LO: To write and calculate numbers in standard form The trick! The number of decimal places you have moved it the number you put 10 to the power of!! 0. 07 = 7 × 10 -2 0. 00941 = 9. 41 × 10 -3 0. 000115 = 1. 15 × 10 -4 Moved the decimal back twice so 10 -2 Moved the decimal back three times so 10 -3 Moved the decimal back four times so 10 -4

LO: To write and calculate numbers in standard form Red Write the following in standard form a) b) c) d) e) f) g) h) i) j) 450 48000 7850 67000000 249 0. 00056 0. 01 0. 00072 0. 0057 0. 000002 Amber Write the following as ordinary numbers. a) b) c) d) e) f) g) h) i) j) 102 6 x 7. 4 x 104 3. 54 x 106 9. 03 x 105 5. 7 x 100 4. 7 x 10 -2 9. 1 x 10 -7 8. 7 x 10 -4 7. 8 x 10 -1 9. 03 x 10 -4 Green Write the following in standard form. a) b) c) d) e) f) g) h) i) j) 80 x 102 220 x 106 8700 x 107 0. 56 x 105 0. 037 x 106 740 x 10 -2 6500 x 10 -3 23 x 10 -4 0. 007 x 10 -4 0. 08 x 10 -5

LO: To write and calculate numbers in standard form Red Write the following in standard form a) b) c) d) e) f) g) h) i) j) 4. 5 x 102 4. 8 x 104 7. 85 x 103 6. 7 x 107 2. 49 x 102 5. 6 x 10 -4 1 x 10 -2 7. 2 x 10 -5 5. 7 x 10 -3 2 x 10 -11 Amber Write the following as ordinary numbers. a) b) c) d) e) f) 600 74000 3540000 903000 5. 7 0. 047 g) 0. 00000091 h) 0. 00087 i) 0. 78 j) 0. 000903 Green Write the following in standard form. a) b) c) d) e) f) g) h) i) j) 8 x 103 2. 2 x 108 8. 7 x 1010 5. 6 x 104 3. 7 x 104 7. 4 x 100 6. 5 x 100 2. 3 x 10 -3 7 x 10 -7 8 x 10 -7

LO: To write and calculate numbers in standard form Use the information below to find out some facts about our world.