Question

Tutorial on significant figure

Answer 1

The total number of digits in the number is called the number of significant figure (S.F.). It is equal to the number of digits written including the last one,even though it's value is uncertain.

Answer 2

The following rules should be followed in counting the significant figures.

(1) All digits are significant except zero at the beginning of the number.
(2) The zeros to the right of the decimal point are significant.

Digit. S.F.
101 3
0.101. 3
0.0101. 3
101.0. 4
101.00. 5

Answer 3

In the above rules the number are expressed in scientific notation. In this notation, every number can be written as N × \(10^n\) where, N is equal to a number with a single non-zero digit to the left of the decimal point and n is an integer. We can write 20,000 in scientific notation as :
2× \(10^4\). (1 S.F)
2.0× \(10^4\). (2 S.F)
2.00× \(10^4\). (3 S.F)

Answer 4

Exact number have an infinite number of significant figure. For example, in 4 pens or 40 copies, there are infinite significant figures as these are exact numbers and can be represented by writing infinite number of zeros after placing a decimal I.e; 4=4.00000 or 40=40.000000

Answer 5

In case of addition and subtraction, the final result should be reported to same number of decimal places as the number carrying minimum number of decimal places to the right. This will become more clear with the following example.

11.1
+1.11
+0.11
-----------
12.32
-----------

Answer 6

Similarly,

3.56
-0.031
-------------
3.529
--------------

Here, 3.56 has minimum number of decimal places of two only so the result after rounding off will be 3.53

Answer 7

In case of multiplication and division , the final result should be reported as having the same number of significant figure as the number with least number of significant figure

This will become more clear with the following example

15.79×6.06=95.6874

Answer 8

Here 6.06 has the minimum number of significant figure that is 3, so the final result after rounding off should have only 3 significant figure,therefore the result will be 95.7

Answer 9

Similarly

\[\frac{5.28 × 0.156×3.00}{0.0428}=57.73458\]

Here all the value have 3 significant figure, so the result should be expressed in 3 significant figure as 57.7

Answer 10

Can you post in pdf, it will be compact then. with few complex examples, which may be handy to everyone.

Answer 11

well that's all the stuff wht i studied in coaching

I don't possess any pdf sorry

Answer 12

@jiteshmeghwal9

You wrote about addition:

"In case of addition and subtraction, the final result should be reported to same number of decimal places as the number carrying minimum number of decimal places to the right. This will become more clear with the following example.

11.1
+1.11
+0.11
-----------
12.32
-----------"

Did you forget to finish by stating that the answer must have the same number of decimal places as the number with the least number of decimal places, so the answer is 12.3?

Answer 13

ohh yup sorry

i forgt to state it

Answer 14

@jiteshmeghwal9
Great explanation, btw.

Answer 15

Thx a lot @mathstudent55