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**SIGNIFICANT FIGURES**

The reliability of a measurement is indicated by the number of digits used to represent it. **To express the measurement more accurately we express it with digits that are known with certainty. These are called as Significant figures.** They contain all the certain digits plus one doubtful digit in a number.**RULES FOR DETERMINING THE NUMBER OF SIGNIFICANT FIGURES**

- All non-zero digits are significant. For example,
**6.9 has two significant figures,**while**2.16 has three significant figures.** - The decimal place does not determine the number of significant figures.
- A zero becomes significant in case it comes in between non zero numbers. For example,
**2.003 has four significant figures, 4.02 has three significant figures.** - Zeros at the beginning of a number are not significant. For example,
**0.002 has one significant figure**while**0.0045 has two significant figures.** - All zeros placed to the right of a number are significant.
**16.0 has three significant figures,**while**16.00 has four significant figures.** - Zeros at the end of a number without decimal point are ambiguous.
- In exponential notations, the numerical portion represents the number of significant figures. For example,
**0.00045**is expressed as**4.5 x 10**in terms of scientific notations. The number of significant figures in this number is 2, while in Avogadro's number (6.023 x 1023) it is four.^{-4} - The decimal point does not count towards the number of significant figures. For example, the number 345601 has six significant figures but can be written in different ways, as 345.601 or 0.345601 or 3.45601 all having same number of significant figures.

**MATH WITH SIGNIFICANT FIGURES**

**(i) ADDITION AND SUBTRACTION OF SIGNIFICANT FIGURES**

The result cannot have more digits to the right of the decimal point than either of the original numbers. 12.11

18.0

1.012

31.122

Here, 18.0 has only one digit after the decimal point and the result should be reported only up to one digit after the decimal point, which is 31.1.

**(ii) MULTIPLICATION AND DIVISION OF SIGNIFICANT FIGURES**

In these operations, the result must be reported with no more significant figures as in the measurement with the few significant figures.

2.5 × 1.25 = 3.125

Since 2.5 has two significant figures, the result should not have more than two significant figures, thus, it is 3.1.**PRACTICE QUESTIONS****Q.1. How many Significant figures in each term? ****(a) 34.6209 ****(b) 0.003048 ****(c) 5010.0 ****(d) 4032.090****Ans. **

(a) 6

(b) 4

(c) 5

(d) 7**Q.2. Solve the following equations using the correct number of significant figures. (a) 34.683 + 58.930 + 68.35112 (b) 45001 - 56.355 - 78.44 (c) 0.003 + 3.5198 + 0.0118 (d) 36.01 - 0.4 - 15**

(a) 161.964

(b) 44866

(c) 3.535

(d) 21

(a) 98.1 x 0.03

(b) 57 x 7.368

(c) 8.578 / 4.33821

(d) 6.90 / 2.8952

(a) 3

(b) 4.2 x 10

(c) 1.977

(d) 2.38

(a) 1.40 x 10

(b) 6.01

(c) 02947.1

(d) 583.02

(a) 3

(b) 3

(c) 5

(d) 5

Here, 18.0 has only one digit after the decimal point and the result should be reported only upto one digit after the decimal point which is 31.1 .

2.5 × 1.25 = 3.125

Since, 2.5 has two significant figures, the result should not have more than two significant figures thus. It is 3.1.

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