Question

How do you determine the number of significant figures in a problem?

Answer 1

Hint:Significant figure is the number that represents the numbers of the digits present in the given value which are meaningful contributors to that value.A significant figure is counted from the first non-zero digit of the given value. It plays a very important role in measurements. In the case of mathematical operations like addition, subtractions, multiplication, and division significant figures play an important role.

Complete step-by-step answer:The significant figures of the problem are determined as follows:
Consider the example as follows:
1. If in the problem it is given that ${\text{25}}{\text{.0}}\,{\text{mL}}$ of a ${\text{0}}{\text{.20}}\,{\text{M}}$${\text{HCl}}$ solution, then the answer should have two significant figures. Because ${\text{25}}{\text{.0}}\,{\text{mL}}$ has three significant figures and ${\text{0}}{\text{.20}}\,{\text{M}}$ has two significant figures.Here, we have to consider the least number of the significant figures hence the answer is in two significant figures for a given problem.
2. In the case of adding and subtracting:
While adding or subtracting the numbers with decimal points consider the least number of the significant figures after the decimal point.For example, the addition of $245.657 + 45.9$ , the answer should have one significant figure after the decimal point. Similar is the case for subtraction.
3. In the case of the multiplication or division:
The answer should have the least number of significant figures as in the problem.For example,$3.2 \times 54.09 \times 0.2$
The answer should be in one significant figure as the least significant figure for the given problem is one.

Note:The rules used to determine the significant figure of the given value are as follows:
1. All non-zero digits present in the given value are significant.
2. The zeros present between the two non-zero digits are also significant.
3. The zeros present before the non-zero digits are called leading zeroes which are non-significant.
4. The zeros present after the non-zero digits are called trailing zeroes, if they are present on the right side of the decimal point then they are significant.
5. The trailing zeros of the whole number are significant only if there is the decimal point is in the given value.