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What are the concepts of significant figures and rounding? How to calculate?

Basic Concept of Significant Figures

The digit that shows precision, in any number or measurement, is termed as the significant figures. Or in other words these are the digits’ number used for expressing a quantity measured or computed.

We can indicate how accurate a number value is using significant figures. Moreover, by expressing a number that goes beyond the real place we measure, we disrupt the integrity of what value that number has.

Thus specific digits with significance or importance and provide further details about the number’s value precisely are the significant figures. In a number, the sig figs also provide significance to certain numbers. 

Significant digits are exceptionally implied in calculations to provide more accurate measurement information and other numerical data. These numbers also help them with very big or very small numbers rounding.

Rules for Significant Figures

Nonzero Integers

The numbers that are non-zero integers, are always considered as significant figures.

Leading Zero

All the zeros that are led by any digit other than zero are known as leading zeros and these zeros are not count as significant digits.

Captive Zero

The captive zeros are however considered as the significant figures these are the zeros present between nonzero digits i.e. natural numbers.

Trailing Zero

The zeros at the right end of the number are termed as trailing zeros. In general, they are considered significant figures if the number has a decimal point or are mentioned in the given statement as significant figure.

Besides to following all these rules, we may also try significant figures calculator with steps to check the significant figure of any number with all possible steps.

Significant Figures’ Rule for Mathematical Operations

The basic rule for calculation is that the precision of a calculated result is restricted by the least accurate measurement involved.

Addition and Subtraction

The result is rounded off to the last common digit which is present farthest from all digits in the right side. 

Multiplication and Division

The result of multiplication and division should be rounded off to the same number of significant figures as the component with the fewest significant figures.


Now you have learnt the basic concept and how many significant figures to maintain, you have to go through the basic concept rounding. As rounding is an important part of significant figures.

During significant figures calculations, we have round the test results to the right number of significant figures. The rounding digit is the final digit that we have to keep during the rounding process. 

While rounding number we make them less accurate, but simpler to calculate and write. Normally the numbers are rounded to a certain digit or any multiple of 10. However, in general situations, the numbers are rounded in the base ten number system.

The rounding can be done in two different ways, when we round off for numbers 0, 1, 2, 3, 4, meaning that the previous number of the digit remains the same, it is known as rounding down.

Whereas, when the numbers 5, 6, 7, 8 and 9 are rounded off, the the preceding digits are increased by 1 and it is termed as rounding up.

How to do Rounding

  • For Whole Numbers

If the numeral to the right of rounding digit is between 1-4, the rounding digit does not change and the digits other than rounding digit become zero. In contrast, if the digits to the right of rounding digit are between 5-9, rounding digit value is increased by 1 while numbers to the right becomes zero.

  • For Decimal Numbers

When rounding the decimal number, the same rule goes just as whole numbers, however except you have to drop the digits to the right of the rounding digit. Consider this example for instance, the number 32.56 rounds to 32.6 if rounding is done to the nearest one-tenth.

Rounding off decimals calculator is the best tool to round off numbers instantly.

  • For Number 5

If the digit to the right of the rounding digit is five, then you have to round up the rounding digit by 1 number if rounding digit is the odd number. On the other hand, if the rounding digit is an even number it remains as it is. Using this method, the last digit will always be even. 

So if the digit is to the right of the rounding digit is 5, you’ll be rounding up half the time and down the other, giving you a more accurate approximation of the real value. With time, your rounding will get more exact.


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