Significant Figures (& d.p.) Rough Estimates Working with Numbers Indices: 4 laws Standard Form Significant Figures (& d.p.) Rough Estimates

Index Laws Simplify: w6 × w2 x3 ÷ x5 = w8 Write down the value of 90 = 1

Index Laws Find the value of: 82 10-3 = 8 x 8 = 64 If 3x = 1 27 what is x? = 8 x 8 = 64 = 1 10 3 = 1 1000 =0.001 x = -3

Index Laws Write the following in index form: = 58 If b3= 8 what is b ? = 58 b = 2

Standard Form Write the following in standard form: 400 000 = 4 x 105 0.000 000 397 = 4 x 105 3.97 x 10-7

Standard Form Work out the following: (2 x 102) × (4 x 105) = 8 x 107 (b) 8× 10 7 2× 10 3 = 8 x 107 = 4 x 104

Standard Form 0.0049 Here are six numbers written in standard form. 2.6 × 105 1.75 × 106 5.84 × 100 8.2 × 10–3 3.5 × 10–1 4.9 × 10–2 (a)Write down the largest number. (b)Write down the smallest number. (c)Write 4.9 × 10–2 as an ordinary number. 0.0049

Significant Figures: Important Zeros in Numbers 5 2 a. Which zeros matter? Are there any we could get rid of and still have the same value? 5 . 2 b. . 5 c. 2 . 5 d. When dealing with Significant Figures, you need to keep any zeros that tell us the value of a number

Rounding to 1 Significant Figure (1SF) 0 . 0 7 6 5 0 . 0 0 1 2 1 . 0 0 9 5 5 or more? 5 or more? 5 or more? Yes No No 0 . 0 8 0 . 0 0 1 1 2 4 1 5 8 7 7 5 5 or more? 5 or more? 5 or more? No Yes Yes 2 0 0 6 0 0 8 0

Rounding to 2 Significant Figure (2SF) 1 4 7 2 1 . 4 2 7 9 0 . 0 5 3 5 5 or more? 5 or more? 5 or more? Yes No Yes 1 5 0 0 1 . 4 0 . 0 5 4 4 2 7 2 8 2 0 4 4 7 8 0 . 0 6 9 6 5 or more? 5 or more? 5 or more? Yes No Yes 4 3 0 0 0 2 0 0 0 0 0 0 . 0 7 0

Rounding to 3 Significant Figure (3SF) 0 . 0 2 6 7 1 3 . 2 9 4 9 3 4 7 2 8 5 or more? 5 or more? 5 or more? No No No 0 . 0 2 6 7 3 . 2 9 3 4 7 0 0 1 3 7 9 8 9 7 4 9 7 8 1 2 . 0 6 9 5 or more? 5 or more? 5 or more? Yes Yes Yes 1 3 8 0 0 9 7 5 0 0 0 1 2 . 1

Rough Estimates By rounding each number to 1 sig. fig, find an approximate answer to : 187 × 196 (b) 315 × 409 5.8 = 200 x 200 = 40 000 = 300 x 400 = 120 000 120 000 ÷ 6 = 20 000

Rounding to 1 Decimal Place (1DP) 4 . 8 3 2 5 4 . 8 4 2 5 4 . 8 5 2 5 or more? 5 or more? 5 or more? No No Yes 4 . 8 4 . 8 4 . 9 4 . 8 7 5 . 2 6 7 1 4 1 . 9 6 7 5 or more? 5 or more? 5 or more? Yes Yes Yes 4 . 9 5 . 3 2 . 0

Rounding to Decimal Places: 2DP 4 . 8 3 2 5 4 . 8 4 6 4 . 8 5 9 5 1 5 or more? 5 or more? 5 or more? No Yes Yes 4 . 8 3 4 . 8 5 4 . 8 6 1 . 6 9 4 9 5 . 2 6 7 1 1 . 8 9 7 5 or more? 5 or more? 5 or more? No Yes Yes 1 . 6 9 5 . 2 7 1 . 9 0

Rounding to Decimal Places: 3DP 4 . 8 3 2 5 4 . 8 4 6 2 4 . 8 5 9 5 5 or more? 5 or more? 5 or more? Yes No Yes 4 . 8 3 3 4 . 8 4 6 4 . 8 6 0 1 . 6 9 4 2 5 . 2 6 2 7 1 . 9 9 9 9 5 or more? 5 or more? 5 or more? No Yes Yes 1 . 6 9 4 5 . 2 6 3 2 . 0 0 0