Significant figures are used to establish the number which is presented in the form of digits. These digits carry a meaningful representation of numbers. The term significant digits are also used often instead of figures. We can identify the number of significant digits by counting all the values starting from the 1st non-zero digit located on the left. For example, 12.45 has four significant digits.
The significant figures of a given number are those significant or important digits, which convey the meaning according to its accuracy. For example, 6.658 has four significant digits. These substantial figures provide precision to the numbers. They are also termed as significant digits.
A number is rounded off to the required number of significant digits by leaving one or more digits from the right. When the first digit left is less than 5, the last digit held should remain constant. When the first digit is greater than 5, the last digit is rounded up. When the digit left is exactly 5, the number held is rounded up or down to receive an even number. When more than one digit is left, rounding off should be done as a whole instead of one digit at a time.
There are two rules to round off the significant numbers:
Q.1: Identify the number of significant digits/figures in the following given numbers.
45, 0.046, 7.4220, 5002, 3800.
Solution:
Number |
Number of Significant digits/figures |
45 |
Two |
0.046 |
Two |
7.4220 |
Five |
5002 |
Four |
3800 |
Four |
Q.2: Write 12.378162 correct to 4 significant digits.
Solution:
See the fifth digit after the decimal point: 12.3781 | 62
The figure after the ‘cut-off point’ is a ‘6’
So we need to round the number up.
Hence, 12.3782 is the answer.