Significant Digits

All measurements involve uncertainty. One source of this uncertainty is the measuring device itself. Another source is your ability to perceive and interpret a reading. In fact, you cannot measure anything with complete certainty. The last (farthest right) digit in any measurement is always an estimate.

The digits that you record when you measure something are called significant digits. Significantdigits include the digits that you are certain about, and a final, uncertain digit that you estimate. Follow the rules below to identify the number of significant digits in a measurement.

Rules for Determining Significant Digits:

Rule 1: All non-zero numbers are significant.

• 7.886 has four significant digits.
• 19.4 has three significant digits.
• 527.266 992 has nine significant digits.

Rule 2: All zeros that are located between two non-zero numbers are significant.

• 408 has three significant digits.
• 25 074 has five significant digits.

Rule 3: Zeros that are located to the left of a measurement are not significant.

• 0.0907 has three significant digits: the 9, the
third 0 to the right, and the 7.

Rule 4: Zeros that are located to the right of a measurement may or may not be significant.

• 22700 may have three significant digits, if the
measurement is approximate.
• 22700 may have five significant digits, if the
measurement is taken carefully.

When you take measurements and use them to calculate other quantities, you must be careful to keep track of which digits in your calculations and results are significant. Why? Your results should not imply more certainty than your measured quantities justify. This is especiallyimportant when you use a calculator. Calculators usually report results with far more digits than your data warrant. Always remember that calculators do not make decisions about certainty. You do. 

Follow the rules given below to report significant digits in a calculated answer.

Rule 1: For Multiplying and Dividing.

The value with the fewest number of significantdigits, going into a calculation, determines the number of significant digits that you should report in your answer.

Rule 2: For Adding and Subtracting.

The value with the fewest number of decimal places, going into a calculation, determines the number of decimal places that you should report in your answer.

Rule 3: For Rounding.

To get the appropriate number of significant digits (rule 1) or decimal places (rule 2), you may need to round your answer.

• If your answer ends in a number that is greater than 5, increase the preceding digit by 1. 

For example, 2.346 can be rounded to 2.35.

• If your answer ends with a number that is less than 5, leave the preceding number unchanged.

For example, 5.73 can be rounded to 5.7.

• If your answer ends with 5, increase the preceding number by 1 if it is odd. Leave the preceding number unchanged if it is even. 

For example, 18.35 can be rounded to 18.4, but 18.25 is rounded to 18.2.

By:
Anjani Kumar Singh.