Name: SI Prefixes: An Overview
Uploaded: 2019-07-19
Duration: 3 min 19 s
Description: Let's focus on SI prefixes and simple unit conversions in this video. Also, let's learn more details on the range of magnitudes of units based on SI prefixes.

Question

What is meant by significant figures? State the rules of finding the significant figures in the sum, difference, product and quotient of two numbers. Support your answer with examples.

Accepted Answer

In the measurement of a quantity, the digits measured accurately and the first doubtful digit are called the significant figures.

The following rules are adopted while dropping figures in rounding off to the appropriate digit:

$(1)$ If the digit to be dropped is less than $5,$ then the preceding digit is retained unchanged. For example, if a number $3.454$ to be rounded off to three significant figures, the digit to be dropped is $4$ which is less than $5$ is not changed. Therefore, it should be written as $3.45 .$

$(2)$ If the digit to be dropped is more than $5,$ then the preceding digit to be retained is increased. For example, $3.458$ is rounded of as $3.46$ to three significant figures.

$(3)$ If the digit to be dropped happen to be $5,$ then the preceding digit to be retained is increase by $1$ if it is odd, but retained unchanged if it is even. For example, $3.445$ is rounded off as $3.46$ to three significant figures and $4.895$ is rounded off as $4.90$ ; but $3.485$ is rounded off as $3.48 .$

Significant figures in addition and subtraction: In adding or subtracting different measured quantities, all other quantities should be rounded off to the same number of significant figures after the decimal point, as contained in the least accurate quantity. For example, suppose we have to add two lengths $27.8 cm and 1.984 cm .$ We shall add this length by simple mathematics as follows:

$27.8 cm + 1.984 cm 29.784 cm$

The sum contains three digits after the decimal point. But the first length $(27.8 cm)$ has only one digit after the decimal point.

On subtracting two nearly equal quantities, the accuracy of difference is decreased. For example, let the measured length of two pieces of wire be $1.57 cm and 1.55 cm .$ Their difference is

$1.57 cm - 1.55 cm 0.02 cm$

Significant figures in multiplication and division : The rule for multiplication and division is quite different from that in addition and subtraction. We first locate the measured quantity having least number of significant figures. Now, we carry out the multiplication or divison and finally round off the result to the same number of significant figures as are contained in the least accurate one. For example, suppose the measured length of a strip is $4.3 cm$ and the breadth is $3.124 cm .$ We, therefore round off $3.124 to 3.12 cm$ and then multiply. Then, the area of the strip is

$4.3 cm \times 3.12 cm = 13.416 {cm}^{2} .$

Hence, we shall write the area is $13 {cm}^{2} .$

The value of $π$ can be written up to unlimited significant figures $(π = \frac{22}{7} = 3.1459) .$

Hence, we shall round off the value of $π$ as $3.142 .$

G L Mittal and TARUN MITTAL Solutions for Chapter: Significant Figures, Exercise 1: QUESTIONS

G L Mittal Physics Solutions for Exercise - G L Mittal and TARUN MITTAL Solutions for Chapter: Significant Figures, Exercise 1: QUESTIONS

Questions from G L Mittal and TARUN MITTAL Solutions for Chapter: Significant Figures, Exercise 1: QUESTIONS with Hints & Solutions

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