Rules for Significant Digits (Figures)
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When you multiply or divide numbers, a calculator will give you more digits than you could
possibly measure; “significant digits” is the scientific method of limiting the number of digits in
a calculated answer.
Significant digits are only used when multiplying or dividing; with addition or subtraction,
simply keep the smallest number of decimals that was in your original math.
The “rule of thumb” for significant digits is that your answer will have the same number of
significant digits as the number with the least number of digits.
What makes a number significant?
o Any non-zero number
o Any non-placeholder or spacer zero.
When is zero not significant?
1. Spacer zeros, or placeholders, are not significant. These zeros hold a numbers “place” to the
correct decimal. If a number can be written in scientific notation without the zero, it is not
significant.
2. The simplest way to remember is that every number is significant except a spacer/placeholder
zero.
Examples:
1. 50.05 = 4 significant digits (sandwich rule).
2. 470.50 = 5 significant digits (ending decimal 0 is always significant).
3. 0.404 = 3 significant digits (first 0 is a placeholder).
4. 0.004 = 1 significant digits (3 placeholder zeros).
5. 0.040 = 2 significant digits (2 placeholder zeros).
6. 0.400 = 3 significant digits (1 placeholder zeros).
7. 400. = 3 significant digits (decimal)
8. 400 = a counting number; infinite significant digits (ignore for SD total)
9. 0.23 and 0.023 both have 2 significant digits
10. 408,300 - 4 significant digits (there is no decimal; the last two zeros are placeholders)
*Whenever you see 0.***, you are dealing with AT LEAST one spacer zero.
*Round at the appropriate significant digit based on the next number (5+).
Sample problems:
1. 2022.5 ÷ 3.5 = 2SD = 577.8571 = 580 no decimal; 0 is a placeholder. (580. = 3SD.)
2. 0.790 ÷ 450.0 = 3SD = 0.0017555 = .00176; 2 placeholders needed for math but do not count
towards total
3. 320.7 + 62.24 = 1 decimal = 382.94 = 382.9
4. 10.2 x 10.4 = 3SD = 106.08 = 106.
After your math, start at the first SD, count out the number of SD’s from the left, then stop and round at
the last SD. Remember your answer cannot have more digits than the number with the fewest digits in
your math (or decimals if +/-). (2012)