SIGNIFICANT FIGURE

When given a number, the digits in it are called significant figures and are obtained by counting from left to the right of the number but zeros to the left or right are not counted, but if zero appears between two digits it will be counted as a significant figure as other digits.

Examples:

 549    has 3 significant figures, counted from 5 to 9

74620 has 4 significant figures, counted from 7 to 2 zero has been excluded because it is at the end to the right side.

0.341  has 3 significant figures, counted from 3 to 1 zero has been excluded because it is at the end to the left side.

19008 has 5 significant figures, counted  from 1 to 8 zeros have been included because they are in the middle of the number.

Note that:

In a number with a decimal point, trailing zeros, those to the right of the last non-zero digit, are significant. Example 23.800 has 5 significant figures

ROUNDING OFF SIGNIFICANT FIGURES

Let’s now understand the position of each significant figure so that we can round off to the required significant figure.

When finding any significant figure we refer to the position of such digit in the number, when counting from left to right. As in 4568 number 6 is the third significant figure so when ordered to round to three significant figures we just take the digit 6 into consideration. Also in number 1257 the digit 2 is the second significant figure, so when ordered to round off to two significant figures we just take number 2 into consideration. Now let’s see the following examples:-

Example 1

Round off 1357 to 2 significant figures.

Solution

The procedure is the same as in rounding off whole numbers what matters is only to know the required significant figure to be figured out. Now check the below steps:-

1.  The digit 3 is the required digit we take it into consideration.

2.  Now the digit next to 3  is 5 so we add 1 in 3 and becomes 4

     (I summarize because procedures are the same as that of whole numbers)

3.  All the rest digits to the to the right side after checking the step above should become 0

4.  Now our answer will be 1400 (to two significant figures)

Example 2

Round off 72954388 to 5 significant figures.

Solution

The procedure is the same as in rounding off whole numbers what matters is only to know the required significant figure to be figured out. Now check the below steps:-

 

1.  The digit 4 is the required digit.  Take it into consideration.

2.  Now the next digit after 4  is 3 so we leave 4 as it is because the next digit  is less than 5 

3.  The rest digits to the right side after checking the step above should become 0

4.  Now our answer will be 72954000 (to 5 significant figures).

 

Example 3

Round off 13.57 to 3 significant figures.

Solution

Don't mind about decimals don't care about it what matters is only to know your number that is required for you to round off.

1.  The digit 5 is the third significant figure so take it into consideration.

2.  Now the next digit after 5 is 7 so we add 1 to 5 and becomes 6

3.  The rest digits to the right side after checking the step above should become 0

4.  Now our answer will be 13.6 (to three significant figures). Note that any zero to the end of decimal is omitted

 

Other examples:

 

64878 to 4 significant figures = 64880 (Check reference in example 1 above)

7651256        to 3 significant figures = 7650000  (Check reference in example 2 above)

5426279442 to 8 significant figures = 5426279400 (Check reference in example 2 above)

27185 to 4 significant figures = 27190  (Check reference in example 1 above)

25.789 to 2 significant figures = 26         (Check reference in example 3 above)

 

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