Rules For Finding Significant Figures With Examples

Rules For Finding Significant Figures With Examples

While finding significant digits, we have to determine important digits that convey the meaning of the given numbers based on accuracy. To find these figures, we have to keep in mind some rules.

1.  All Non-Zero Digits are Significant Figures

The digits other than zero are non-zero digits. For example, 1, 2, 3, 4, etc. are non-zero digits. If we have a reading of 6745, it contains 4 non-zero digits. It means that it has 4 significant figures.

2.  Zeroes Between Non-Zero Digits Are Also Significant Figures

If we are taking a reading, we can get zeroes. For example, we can get readings as 1008, 20187, 789001, etc. These readings show that these zeroes are in between non-zero digits. According to the rules for finding significant figures, these zeroes are also significant. In the readings 1008, 20187, and 789001, there are 4, 5, and 6 significant figures respectively.

3. Rules For Zeroes on the Right and Left Side of Non-Zero Digits

For example, we have two readings 00756 and 89400. In the first reading 00756, we have two zeroes on the left side of the non-zero digits. These zeroes are non-significant digits. Therefore, we have only 3 significant figures in this reading. On the other hand, in reading 89400, we have zeroes on the right side of the non-zero digits. According to the rules for finding significant figures, these zeroes are significant. Therefore, this reading has 5 significant figures.

If we want to understand this concept more accurately, we have to see the last non-zero digit from the right and left sides. In the reading 00756, 7 is the last non-zero digit from the left side. All the zeroes after this non-zero digit are non-significant. Similarly, we should also see the last non-zero digit from the right side. In reading 89400, 4 is the last non-zero digit from the right side. All the zeroes after this non-zero digit are significant.

4. Rules For Zeroes on Right and Left Side of Decimal Points

To understand this rule for finding significant figures, we also take two examples. These examples are 000.678 and 78.000. In the first example 000.678, we have three zeroes on the left side of the decimal point. According to the rules for finding significant figures, these zeroes are non-significant. Therefore, there are only 3 significant figures in this example. On the other hand, in the example 78.000, we have three zeroes on the right side of the decimal point. These zeroes are significant. Therefore, there are 5 significant figures in this example.

Rounding Off Significant Figures

To get more precise results, we may have to round off these figures. For this reason, we have to keep in mind some important things.

♦First of all, we have to know up to which digit we want to round off the given number. For example, we have a number 67.546712 and we want to round off this number up to two digits after the decimal point. It means that we have to skip 6712 from this number.

♦Secondly, we have to see the digit just after the digit that we want to round off. In this example 67.546712, we have to see the digit after 4 and this digit is 6.

♦If this digit is less than 5, we can round off this digit without making any changes. For example, if we have the number 89.45341 and we want to round off this number up to two decimal places, we will get 89.45. Its reason is that after the second digit, we have 3 and it is less than 5. That’s why we can skip the digits after two decimal places without making any changes.

♦If this digit is 5 or greater than 5, we have to add 1 in the last digit. In the previous example 67.546712, we have 6 after two decimal places. It is greater than 5. Therefore, we have to add 1 to the number and our answer will be 67.55.