Significant figures (or significant digits) refer to the digits in a number that carry meaning or contributes to the number's precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal part.
It implies that:
Consider the examples below:
Example 1
1. The number 523 has 3 significant figures, 5, 2 and 3. with 5 being the first significant figure as it holds the highest value (500), 2 is the next significant figure after 5, and 3 is the last significant figure as it holds the least value, (3).
2. The number 0.00523 has 3 significant figures (the leading zeros are not significant).
3. The number 1000 has 1 significant figure (unless specified otherwise with a decimal point, e.g., 1000.0 would have 5 significant figures).
Rounding Numbers to Significant Figures
To express a number to a specific number of significant figures:
1. Identify the number of significant figures required.
2. Round the number according to the specified significant figures.
If necessary, adjust the trailing digits.
Examples 2
1. 3456 to 2 significant figures becomes 3500.
2. 0.03456 to 2 significant figures becomes 0.035.
3. 987.654 to 4 significant figures becomes 987.7.
Example 3
Round the following to 5 significant figures:
1. 637407
2. 470114924
3. 0.0005897
4. 1.99876
5. 2.77893
Solution
1. \(637407 \implies 637410 \ to \ 5 \ significant \ figures\)
2. \(470114924 \implies 470110000 \ to \ 5 \ significant \ figures\)
3. \(0.0005897 \implies 0.00058970 \ to \ 5 \ significant \ figures\)
4. \(1.99876 \implies 1.99880 \ to \ 5 \ significant \ figures\)
5. \(2.77893 \implies 2.77890 \ to \ 5 \ significant \ figures\)
Example 4
Round the following to 4 significant figures:
1. 637407
2. 470114924
3. 0.0005897
4. 1.99876
5. 2.77893
Solution
1. \(637407 \implies 637400 \ to \ 4 \ significant \ figures\)
2. \(470114924 \implies 470100000 \ to \ 4 \ significant \ figures\)
3. \(0.0005897 \implies 0.0005897 \ to \ 4 \ significant \ figures\)
4. \(1.99876 \implies 1.999 \ to \ 4 \ significant \ figures\)
5. \(2.77893 \implies 2.779 \ to \ 4 \ significant \ figures\)
Example 5
Round the following to 3 significant figures:
1. 637407
2. 470114924
3. 0.0005897
4. 1.99876
5. 2.77893
Solution
1. \(637407 \implies 637000 \ to \ 3 \ significant \ figures\)
2. \(470114924 \implies 470000000 \ to \ 3 \ significant \ figures\)
3. \(0.0005897 \implies 0.000590 \ to \ 3 \ significant \ figures\)
4. \(1.99876 \implies 2.00 \ to \ 3 \ significant \ figures\)
5. \(2.77893 \implies 2.78 \ to \ 3 \ significant \ figures\)
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