[Mathematic Form 4] To Round Off Numbers

To round off number to an appropriate number of significant figures, you may use the following steps:

1. Identify digit x that is to be rounded off.
2. Is the digit after x greater than, or equal to, 5?
3. If it is either greater than, or equal to, 5, add 1 to x.
4. If it isn't, then x remains unchanged.
5. Do the digits after x lie before or after the decimal point?
6. If before, replace each digit with a zero.
7. If after, drop the digits.

Let's try the steps on a few examples.

Suppose we have to round off the following numbers:

a) 34,782 to 1 significant figure
Solution:
34,782
The digit to be rounded off is 3. The digit after 3 is 4. 4 is less than 5.
Therefore, 3 remains unchanged and each digit to the right of 3 (4, 7, 8, 2) is to be replaced with zero.

34,782 = 30,000 (1 significant figure)

b) 54.78 to 3 significant figures
Solution:
54.78
The digit to be rounded off is 7. The digit after 7 is 8. 8 > 5.
Therefore, add 1 to 7 and drop the digit 8 because it lies after the decimal point.

54.78 = 54.8 (3 significant figure)

c) 0.0050327 to 2 significant figures
Solution:
0.0050327
The digit to be rounded off is 0. The digit after 0 is 3. 3 is less than 5, so leave 0 unchanged. Digit 2 and 7 are after the decimal point, so drop the digits.

0.0050327 = 0.0050 (2 significant figure)

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• 7245.9 to be rounded off to 2 significant figure (sf) is 7,200.
• 0.0011056 to be rounded off to 3 significant figure (sf) is 0.00111.
• 986,468 to be rounded off to 1 significant figure (sf) is 1,000,000.
• 5.00402 to be rounded off to 5 significant figure (sf) is 5.0040.
• 67.9081 to be rounded off to 4 significant figure (sf) is 67.91.