1. Accuracy

2. Rounding
Rounding is a way to shorten numbers that have too many decimal places
E.g.
You can round 1.45 to the nearest whole number
This is 1
You can round to 1 decimal place
This is 1.5

3. The Rules
You round (the last number we keep) up if the cut off number is 5 or above
E.g.
1.5 to the nearest whole number is
2 (5 was the cut off number)
The number we keep stays the same if the cut off number is under 5
E.g to 1 d.p.
Is 1.4

4. Try these; Round these to the nearest whole number; 14.85 30.6 79.5
Round these to 1 d.p.
4.682
29.950
50.97
Round these to 2 d.p.
73.592
0.3081
99.999

5. Answers 15 31 80
4.7 30 51
73.59
0.31
100

6. Significant Figures You can also round to significant figures
The rules are:
The first number is significant unless it is 0
If it is 0 then the first number that isn’t 0 is the first significant figure
E.g.
What is the first significant figure for these numbers
37.8 3
0.0538 5 2
What is 37.8 to 1 s.f.?
40 (the 3 is rounded because of the 7)

7. Try these Round these to 2 s.f. 657 499 0.05982 Round these to 3 s.f.
30303
89950
20785

8. Answers
660
500
0.06
30,300
90,000
20,800

9. Estimating When we estimate we usually round to 1 s.f.
E.g. What is 93 x 11
90 x 10
900
What is 250 x 123
300 x 100
3,000

10. Upper and Lower Limits
When we measure things they have been rounded up or down
E.g. A metre ruler is usually correct to or 4 s.f.
It could be as big as:
(this is rounded to 5 s.f.)
You add 5 on to the end of the number for the upper limit
It could be as small as:
99.95

11. Try these; Write down the upper and lowers limits for these:
The length of a pencil is 16cm correct to the nearest cm.
The weight of a box is 23.6 lbs correct to 1 d.p.
The weight of a baby is 4.2 kg correct to 1/10 of a kg
A journey took 75 minutes correct to the nearest minute

12. Answers 15.5 to 16.5 cm 23.65 to 23.55 lbs 4.25 to 4.15 kg
75.5 minutes to 74.5 minutes

13. Standard Form
This is a quick way of writing really long numbers e.g. a googol is 10 with 100 zeros after is but it can be written as 1 x 10100
There are rules for using standard form;
It has to be written as y x 10z (this is the Exp button on your calculator)
Y has to be between 1 and 10
The z tells you how many numbers come after the first number

14. Really Big Numbers
4 x 106
4,000,000
5 x 103
5,000
5.1 x 103
5,100
1.745 x 104
17,450
1.745 x 102
174.5
11 x 103
This is written wrong and should be 1.1 x 104

15. Try these; Write these as ordinary numbers; 3.05 x 102 49 x 106
Write these in standard form;
70,000
450,000
10,000,000,000
378,000,000

16. Answers 305 This is written wrong 9it should be 4.9 x 107 5,700
7,480,000,000
7 x 104
1 x 1010 or 10 x 109
3.78 x 108

17. Really Small Numbers
Standard form can be used for really small numbers like the mass of an atom or the size of a cell etc.
Decimals are written as 10-z
E.g. 7.8 x 10-3
This is
There are three zeros before the 78

18. Try these; Write these as an ordinary number; 2.6 x 10-3 5.7 x 10-5
Write these numbers in standard form;
0.006
0.035

19. Answers
0.0026
6 x 10-3
3.5 x 10-2
5.6 x 10-4
6.082 x 10-4