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

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

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

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

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

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

7. Standard Form 0.0049 Here are six numbers written in standard form.
2.6 × × × × 10–3 3.5 × 10– × 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

8. Significant Figures: Important Zeros in Numbers5 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

9. Rounding to 1 Significant Figure (1SF)
5 or more?
5 or more?
5 or more?
Yes No No 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

10. Rounding to 2 Significant Figure (2SF)
5 or more?
5 or more?
5 or more?
Yes No
Yes
1 . 4
5 or more?
5 or more?
5 or more?
Yes No
Yes

11. Rounding to 3 Significant Figure (3SF)
5 or more?
5 or more?
5 or more? No No No
5 or more?
5 or more?
5 or more?
Yes
Yes
Yes

12. Rough Estimates
By rounding each number to 1 sig. fig, find an approximate answer to :
187 × 196
(b) ×
= 200 x 200 =
= 300 x 400 =
÷ 6 =

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

14. Rounding to Decimal Places: 2DP
5 or more?
5 or more?
5 or more? No
Yes
Yes
5 or more?
5 or more?
5 or more? No
Yes
Yes

15. Rounding to Decimal Places: 3DP
5 or more?
5 or more?
5 or more?
Yes No
Yes
5 or more?
5 or more?
5 or more? No
Yes
Yes