Significant Figures Calculator

What are significant figures in maths?

The crucial or important digits that accurately represent the meaning of a certain number are known as the significant figures of that number. 6.658, for instance, has four significant digits. These huge amounts give the numbers accuracy. Additionally, they are known as significant digits. The first non-zero digit of a number is considered the first significant figure when counting significant figures. The second digit is considered the second significant figure, and so on. The decimal point may be followed by a significant figure to the left or right of it. Similar to rounding to a number of decimal places, units, tens, hundreds, and thousands, significant figure rounding involves finding the right significant figure to give the desired level of accuracy.

What are rules for significant figures?

1. Every non-zero number has meaning. Due to the fact that there are no zeros in any of the digits, the number 33.2 has THREE significant figures.
2. There IS significance for zeros in between two non-zero numbers. There are FOUR important numbers in 2051. The zero is in the range of 2 and 5.
3. Leading zeros don't matter. They serve only as "place holders." There are only TWO major figures in the number 0.54. Additionally, 0.0032 contains TWO significant figures. The zeros are all leading.
4. Right after the decimal, the trailing zeros ARE important. In 92.00, there are FOUR major figures.
5. There is significance to the trailing zeros in a whole integer with the decimal indicated. It's customary to leave out the decimal point at the end of a number. However, this decimal signifies a significant zero by tradition. For instance, the value "540." shows that the trailing zero IS important because it contains THREE significant figures.
6. Trailing zeros in a whole number that aren't represented by a decimal point are not important. Writing "540" alone implies that there are only TWO significant numbers in this value and that the zero is NOT significant.
7. The number of significant figures for exact numbers is INFINITE. For numbers that are definitions, this rule is applicable. For instance, 1 metre is equal to 1.00 metres, 1.00 metres, 1.00 metres, 1.00 metres, etc.

Why to use significant figures?

Science and measurement frequently employ significant figures. They serve as a means of expressing how precise a measurement is. There are more accurate means of measuring than others. Imagine you had two scales, one that could measure weights to the nearest gramme and another that could measure weights to the nearest hundredth of a gramme. In both cases, a measurement of 3 grammes would have distinct connotations. Because you only know that the measurement is accurate to 1 gramme, you would only record the initial measurement as 3 grammes. You might write down the second measurement as 3 grammes. This indicates that the measurement was precise to one hundredth of an inch. These additional significant numbers are used to record the measurement's accuracy.

How rounding significant figures works?

By omitting one or more digits from the right, a number is rounded off to the necessary number of significant digits. The last digit kept should not change if the first digit in the left column is less than 5. The last digit is rounded up when the first digit exceeds 5. When there are precisely five digits remaining, the number retained is rounded up or down to an even number. Rounding off should be done as a whole rather than one digit at a time when there are multiple digits left.

To round off the significant numbers, there are two rules. First, we must determine the digit up to which the rounding off should be done. We must eliminate all the digits on the right side if the number following the rounding off digit is less than 5. However, if the digit immediately following the rounding off digit is more than 5, we must add 1 to it and disregard the other numbers on the right side.

What are 3 significant figures?

The digit following the second significant figure is known as the third significant figure of a number. It follows that this is accurate even if the digit is zero. Therefore, the third and fourth significant values of 20,499 are 4, and the third and fourth significant figures of 0.0020499 are 9, respectively. The same as when rounding to three decimal places, we also round a number to three significant figures. For three digits, we start counting with the first non-zero digit. Next, we round the final digit. Any empty spaces to the right of the decimal point are filled with zeros. We require them to store the proper place value for the significant digits, which is why they are necessary.

How to do significant figures addition, subtraction, multiplication and division?

When applying algebraic operations on measured quantities, we make sure the outcome is not more accurate than the value with the lowest stated precision. As a result, the number of significant figures in our calculation's outcome should be equal to the number of significant figures in the least precise value.

After rounding off, the output should have the same number of significant figures as the reading with the fewest significant digits.

As an illustration, 7.9391 + 6.263 + 11.1 = 25.3021

The answer will be rounded so that it also has three significant digits because the least precise value, 11.1 has three significant digits. i.e. 25.3.

For instance, 12.50 x 169.1 = 2113.75

There are four important digits for each digit. As a result, the final solution is rounded off to include only 4 significant digits, hence the answer will be 2114.

Three significant figures examples

Due to the fact that 3 is the first non-significant digit, 654.389 becomes 654.

65.4389 changes to 65.4.

Due to the need for the zeros to hold the place values, 654,389 becomes 654,000.

Due to the fact that 6 is the first non-significant digit, 56.7688 becomes 56.8.

0.03542110 is changed to 0.0354. Keep in mind that having three significant figures differs from having three decimal places, which would give us the value 0.035.

Due to the final zero being a significant number and being the third in the series 4, 1, 0, 3, 2, 0.0041032 becomes 0.00410.

We round the third significant figure from 9 to 10, changing 45.989 to 46.0. As a result, the third digit becomes zero and the preceding digit, 5, is increased to 6.