What are the rules for determining significant figures?

The significant figures also referred to as significant digits are utilized by the scientist, engineer, chemist, and economist to present the value of a physical quantity, all the digits that represent the value of a quantity are actually not important so that keeping in view the precise and accurate value they count the few important digits to present a particular data of the numbers. For example, if somebody asks you what is your age, then evaluating your age more important is your month of birth and the year which are more important or say a more significant part of your birth date since month and year are required to calculate your age.

The parts of the number that increase the accuracy of measurement are known as significant part and the digits involved in it is known as significant digits. The number of significant digits can be identified by counting the digits from the first non-zero digit located on the left of the decimal.

The significant digits give precision and accuracy of observation in the form of a number, precision is the closeness of two observations of the same quantity of an experiment under the same condition while accuracy is the closeness between the observation and the actual value of the same quantity. Scientists and mathematicians have propounded the rule of determining the significant digits of a number that are following.

In measuring the significant digits one has to take care of the following rules

All the digits except zero are always significant. For example, 197526 contains six significant digits.
Any zeros placed in between any two non-zero digits are significant. For example, 12.008 contains five significant digits.
If zeros are placed both on the right of a decimal point and left of a non-zero digit, they are not significant. For example, 0.0045 contained two significant digits.
If zeros are placed on the right of the decimal and not have a non-zero digit after that, then it is significant. For example, 90.00 contains four significant digits.
Zeros placed on the right of the last non-zero digit after the decimal point are significant. For example, 0.00254200 contains six significant digits.
Zeros that are placed on the right of the last non-zero digit are significant when they come from a measurement. For example, 5460 m contains four significant digits.

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Rounding off the significant digits

(i) If a number involves significant digits needed to be rounded off to a certain number of decimal places, then exclude all the digits after that number if the next digit is less than 5. As an example rounding off the figure 23.084621 up to 4 places is 23.0846 and rounding of up to 3 places is 23.085.

What are the rules for determining significant figures?

Rounding off the significant digits

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