Estimation & Approximation

Estimation & approximation
BTEOTSSSBAT:
Use estimation to check answers
Write numbers to 1, 2or 3 significant figures

Key terms
Approximation
Estimation
Significant figures

Write approximations for these numbers
18.9
10.2
102.4
172
1005
1779.3
0.45

Significant figures
The first significant figure of a number is the first non-zero number from the left.
Here the 5 is the first significant figure
0.054
1054
And here the 1 is the first significant figure
Zeros are only non-significant if they are sandwiched between tow other numbers

0.074
0.074
Find the first significant figure (7)
Look a the next number 4 – if it is 5 or more increase the 7, if it is less than five leave the 7 alone
0.07
So 0.074 to 1 sig fig is 0.07

704
704
Look a the next number 0 – if it is 5 or more increase the 7, if it is less than five leave the 7 alone.
It’s not a decimal so all the other digits need to be zeros to keep the place value
700
So 704 to 1 sig fig is 700

0.076
0.076
Look a the next number 6 – if it is 5 or more increase the 7, if it is less than five leave the 7 alone
0.08
So 0.076 to 1 sig fig is 0.08

751
751
Look a the next number 5 – if it is 5 or more increase the 7, if it is less than five leave the 7 alone.
800
So 751 to 1 sig fig is 800

Write these numbers to 1 significant figure
18.9
20
10.2
10
102.4
100
172
200
1005
1000
2000
1779.3
0.5
0.45

To round to 2 significant figures:
Ignore all the zeros at the beginning
Find the second significant figure from the left
If the number to the right is 5 or more, increase the second number by 1
Turn all the other digits to the right to zero.

For example
Round 2684 to 2 significant figures
There are no zeros at the beginning
Find the second significant figure from the left:
The second significant figure is 6
2684
The number to its right is 8, which is greater than 5, so increase 6 by 1 to make 7
Turn all the remaining digits to zero
Answer
2684 to 2 significant figures is 2700.

Another way of looking at it is to decide if 2684 is nearer to 2700or 2600
2684
2600
2700
2650

Writing numbers to 1 significant figure can help with checking answers and with estimating
For example
Calculate:
48 x 102
52.4
Using a calculator:
4896 = 93.43511….
52.4
Estimating – using 1 sig. fig.:
48 x 102 =
52.4
50 x 100 =
50
100
Check

Writing numbers to 1 significant figure can help with checking answers and with estimating
For example
Calculate:
5.4x 19
2.4
Using a calculator:
102.6 = 42.75
2.4
Estimating – using 1 sig. fig.:
10
5 x 20=
2
50
Check

Now try these
Estimate:
140 x 19
2.1
Estimate:
540x 1.92
3.9
Estimate:
1040x 192
48

Example
Round 0.00854 to 2 significant figures
Ignore the zeros at the beginning
The second significant figure is the 5
0.00854
The number to the left is 4, which is less than 5, so keep the 5 as a 5
The 4 to the left becomes as zero
So write 0.00854.
Answer
0.00854 to 2 significant figures is 0.0085

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Estimation & Approximation

by Steve Bishop on Oct 09, 2009

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Estimation & Approximation — Presentation Transcript