Significant figures are one of the first concepts that any JEE student comes across when starting preparation for JEE Physics. It is a fundamental topic under the chapter “Units & Measurements” for Physics. In this post, we will simplify the process of calculating significant figures in any measurement with a few easy-to-follow rules.

Significant Figures, also called Significant digits, are a simple, yet significant concept in the Science of units & measurements. Significant figures are a way of expressing the precision or accuracy of a measured or calculated quantity. They are important in science and engineering to convey the reliability/precision of a number. Significant figures (SF) help communicate how well a measurement was made or how precise a calculation is. When performing calculations with numbers, it’s important to pay attention to significant figures to ensure that your final result reflects the appropriate level of precision.

#### Rules of Significant Figures

There are many rules for determining Significant Figures (SF). This article gives about 10 rules for determining significant figures. However, to keep things simple, we will boil down these to as few rules as possible. So, here are the rules you need to keep in mind while determining significant figures.

##### Rule 1. All non-zero digits and zeroes between non-zero digits are significant.

You need to check the first and last non-zero digits in the number. All numbers between the first(left-most) and last(right-most) non-zero digits are significant.

Examples:

- 1234 – 4 SF (1,2,3,4)
- 12034 – 5 SF (1,2,0,3,4)(0 comes between non-zero digits, so it is significant)
- 120.34 – 5 SF (1,2,0,3,4)
- 0.123 – 3 SF (1,2,3) (Decimal point makes no difference in this rule.)

##### Rule 2. All Zeroes to the right of the decimal point are significant.

After checking Rule 1, you need to apply Rule 2. In this rule, you need to check for zeroes to the right of the decimal point. All these zeroes are significant.

Examples:

- 190 – 2 SF (2,9) (only non-zero digits are counted as SF)
- 1.90 – 3 SF (2,9,0)
- 10.90 – 4 SF (2,0,9,0)(2 & 9 are the first & last non-zero digits, so all digits in between 2,0,9 are significant. 0 lies to right of decimal, so it is also significant)

##### Rule 3: All Zeroes to the left decimal point and right of the last non-zero digit are significant.

After Rules 1 & 2, time to apply Rule 3. Here, we check if there are any zeroes between the last non-zero digit and the decimal point.

Examples:

- 390. – 3 SF (3,9,0) (0 is counted because it is to the left of the decimal point and right of the last non-zero digit 9)
- 390 – 2 SF (3,9) (0 is not counted because there is no decimal point)
- 3900. – 4 SF (3,9,0,0) (both zeroes are counted as they are to the left of decimal and right of the last non-zero digit 9)

#### Additional Rules

Apart from the above rules, there are a few exceptions to be followed while calculating significant figures.

- Stoichiometric coefficients and unit conversion factors have an infinite number of Significant figures.
- For measurements using logarithms, such as pH, the number of significant figures is the number of digits to the right of the decimal, including all zeros.

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