Significant Figures

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It was stated in a newspaper that the attendance at the MCG(Melbourne Cricket Ground) for a football match was 64,000. But a friend who was attending the same match said the crowd was 64,492. The information from both sources are correct, but it was given to a different degree of accuracy.

64,492 might have been the exact number. When we round off 64,492 to two significant figures, it is 64,000.

The first non-zero digit, reading from left to right in a number, is the first significant figure.

e.g. In 64,492 , 6 is the first significant figure.(sig.fig.) When we round off 64,492 to two sig. figs, that means in the answer we should have two non zero figures.The third figure(which is 4) is less than 5, so we drop them to zeros.

Let's round off 64,492 to:
(a) 1 significant figure      which is 60,000
(b) 2 significant figures     which is 64,000
(c) 3 significant figures     which is 64,500
(d) 4 significant figures     which is 64,490
(e) 5 significant figures     which is 64,492

The accuracy of the answer will depend on the number of significant figures. The answer will be more accurate, if it is given to a higher number of significant figures.

64,492 is the most accurate answer and it is given to 5 sig. figs.

*** The trailing zeros in a whole number are not significant.There are used to keep the other figures in there correct places.
eg. 64000     6 and 4 are significant not the zeros.

*** The leading zeros in a decimal are not significant. There are used to keep the other figures in there correct places.
eg. 0.000054 ,   only 5 and 4 are significant.

***The zeros between the figures are significant.
eg. 30.05    each figure is significant. There are 4 sig.figs.

*** The last zero in a decimal is significant.
eg. 3.20each figure is significant. There are
      3sig.figs.

eg. 0.50, 5 and last zero are significant.There are
       2 sigfigs

Examples

Example 1:
Let's round off 92.810576 to:

(a) 1 significant figure	9 is the first non-zero digit, that means 9 is the first sig. fig. In 92.810576 the second figure 2 which is less than 5, so we round down the number. When we round off 92.810576 to 1 sig. fig. is 90
(b) 3 significant figures	In 92.810576, 928 are the first three digits, the next figure 1 which is less than 5, so we round down the number. When we round off 92.810576 to 3 sig.figs. is 92.8
(c) 6 significant figures	In 92.8105\|76, the first six significant numbers are 92.8105. The zeros between the figures are significant. the next figure 7 which is more than 5, so we round up the number. When we round off 92.816057 to 6sig. figs. is 92.8106

Example 2:
Let's round off 0.0046753 to:

(a) 1 significant figure	In 0.0046753, 4 is the first sig.fig. The leading zeros are not significant, but they are used to keep other figures in their correct places.In the above number the figure to the right of 4, is 6 which is more than 5, so we round up the number. When we round off 0.0046753 to 1 sig.fig. is 0.005
(b) 2 significant figures	When we round off 0.0046753 to 2 sig.figs. is 0.0047
(c) 4 significant figures	In 0.0046753, 4 is the first sig.fig. The leading zeros are not significant, but they are used to keep other figures in their correct places.In the above number 5 is the 4th significant figure. The figure to the right of 5 is 3 which is less than 5, so we round down the number. When we round off 0.0046753 to 4 sig.figs. is 0.004675

Have a Go

Problem 1
Give each answer correct to the number of sig. figs. indicated in each of the brackets.

(a) 3.185×0.49 (2sig.figs.)

(b) 0.485 ÷ 0.0638
     (3sig.figs.)

Problem 2
State the number of sig. figs. in each of the these numbers.

(a) 35

(b) 0.072

(c) 3.040

(d) 3000

Practice Questions

Question 1
Calculate the answer to 1 sig.fig.

0.0075 ÷ 0.0000715

Question 2
Calculate the answer to 3sig.figs.

0.0075 ÷ 0.0000715

Question 3
State the number of sig.figs

350.701

Question 4
State the number of sig.figs

67.030 kg

Question 5
Select the most precise measurement.

3.2m, 3.20m, 3.195m

Question 6
Select the most precise measurement.

9.4, 0.0001, 5.03

Solution 1

(a) 3.185 × 0.49           (2 sig.figs.)
You can use a calculator to multiply the numbers.
      3.185 × 0.49 = 1.56065 We want the answer to 2sig.figs.
In 1.5|6065, 1 is the first sig.fig. 5 is the 2nd sig.fig.The number to the right of 5 is 6, which is more than 5, so we round up the number.
The answer is 1.6

(b) 0.485 ÷ 0.0638    (3 sig.figs.)
You can use a calculator to divide the numbers.
    0.485 ÷ 0.0638 = 7.6018808 We want the answer to 3sig.figs.
In7.60|18808, 7 is the first sig.fig, 6 is the 2nd sig.fig, 0 is the third sig.fig. The number to the right of 0 is 1, which is less than 5, so we round down the number.
The answer is 7.60

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Solution 2

State the number of sig. figs. in each of the these numbers.

(a) 353 3 sig.figs.

(b) 0.072 2sig.figs., the leading zeros in a decimal are not significant.

(c) 3.040 4sig.figs., the zeros between the numbers are significant and also the last zero in a t decimal is significant.

(d) 3000 1sig.fig.,the trailing zeros in a whole number are not significant.

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