Standard Form

1. Standard Form 3 x 105 = 3 x 100 000 = 300 000 4.36 x 103 = 4.36 x 1 000 = 4360 Scientific Notation

2. 10 000 000 = 10 7 10x10x10x10x10x10x10 1 000 000 = 10 6 100 000 = 10 5 10 000 = 10 4 or x 10 x 10 x 10 x 10 1000 = 10 3 or x 10 x 10 x 10 100 = 10 2 or x 10 x 10 10 = 10 1 or x 10 1 = 10 0 or x1 0.1 = 10 -1 or ÷10 0.01 = 10 -2 or ÷10 ÷10 0.001 = 10 -3 or ÷10 ÷10 ÷10 0.000 1 = 10 -4 or ÷10 ÷10 ÷10 ÷10 0.000 01 = 10 -5

3. 1 2 3 4 5 250 000 = 2.5 x 10 x 10 x 10 x 10 x 10 25 250 2500 25 000 250 000 Standard Form 2.5 x 10 5 = 62 370 = 6.237 x10 4 3 162 = 3.162 x10 3 0.26 = 2.6 x10 -1

4. Rewrite the following as ordinary numbers 7 x 10 4 4.39 x 10 6 7.21 x 10 0 3.2 x 10 -2 1.82 x 10 -5 5.09 x 10 -1 Give the following in Standard form: 569 2 817 539 270 5.69 x 10 2 2.817 x 10 3 5.3927 x 10 5 9.3 0.395 0.003 68 9.3 x 10 0 3.95 x 10 -1 3.68 x 10 -3 70 000 4 390 000 7.21 0.032 0.000 0182 0.509

5. Calculating with numbers in standard form Distance of 3.6 x 107 kilometres at speed of 1.8 x 103 km/s 3.6 x 107 D S T T = 1.8 x 103 3.6 107 = 7 - 3 x 1.8 103 = 2 104 seconds x Speed of 3.27 x 102 m/sec for 1 hour 3.27 x 6 1952 x 6 117.12 D = 3.27 x 102x 60 x 60 = 3.27 x 6 x 6 x 10 2x 10 x 10 = 117.12 x 10 4 4 + 2 = 1.1712 x 10 6