Significant Digits Rules (aka sig digs)
leading zeros
0.000052008000
trailing zeros
sandwiched zeros
Rule 1: Reading from the left, start counting at the first NON-ZERO number.
All NON-ZERO numbers are significant.
1,334 = 4 sig digs
0.00489 = 3 sig digs
Rule 2: Leading zeros are NOT significant
0.00128 = 3 sig digs
Rule 3: Sandwiched zeros ARE significant
0.070203 = 5 sig digs
0.87 = 2 sig digs
7,400,0123 = 8 sig digs
Rule 4: Trailing zeros after the decimal ARE significant
1.0900 = 5 sig digs 4.0 = 2 sig digs
Rule 5: Trailing zeros without a decimal are NOT significant [unless EXACT]
100 = 1 sig dig
100. = 3 sig digs
100.0 = 4 sig digs
Rule 6: Digital measurements - All digits ARE significant EXCEPT leading zeros
Rule 7: Analog measurements – All digits known with certainty + an estimated digit ARE
significant
Rule 8: Multiplication & Division - Count the number of significant digits in each part of the
problem. The answer has the same number of significant digits as the LEAST precise
value. Round the answer to the number of significant digits
13.1 (3 sig digs) x 9.8 (2 sig digs) = 128.38 (round the answer to 2 sig digs) = 130
Rule 9: Addition & Subtraction – count the number of DECIMAL places. The answer has the
same number of DECIMAL places as the number with the LEAST number of decimal
places. Round the answer to the least number of decimal places.
1.346 (3 decimal places) + 67.1 (1 decimal place) = 68.446 (round to 1 decimal place) = 68.4
Rule 10: In calculations, EXACT numbers or conversions do not count towards significant digits
6 rulers (exact)
1,000 g = 1kg (exact)
60 sec = 1 hr (exact)
Rule 11: Scientific Notation – all the rules apply to the coefficient (not the 10x)
1.056 x 108 = 4 sig digs
4.0 x 10-459 = 2 sig digs
4.00 x 1023 = 3 sig digs
Rule 12: In multi-step calculations, keep at least one extra digit and round at the very end. If
your calculator has stacks, use stacks for multistep calculations and apply sig digs to the
final answer.