Uncertainty and Significant Digits

2.4-2.5

How long is the nail?

Uncertainty

• Every measurement has some degree of uncertainty.

• When making analog (non-digital) measurements, you record all certain digits and the first uncertain digit.

Significant Digits

• The numbers recorded in a measurement are significant digits.

• More sigfigs = more precise (exact)

Determining Sigfigs

• Any nonzero digit IS significant• Leading zeros NEVER significant• Captive zeros ALWAYS significant• Trailing zeros ARE significant IF there is

a decimal• EXACT numbers have UNLIMITED

sigfigs– Defined numbers or counting numbers

0.00220500

Leading zeros-zeros before the first nonzero digit

Captive zero-zero between two nonzero digits

Trailing zero-zero after the last nonzero digit

How many sigfigs are there in 0.000304 g?

3

0.0

How many sigfigs in 1.270 x 102

4

0.0

10900.

5

0

1000

1

0.0

0.09020

4

0.0

Sigfigs in Calculations

• Rounding off• Don’t round off until after the final calculation.• Multiplication or division: # of sigfigs in

answer = least number of sigfigs of measurements

• Addition or subtraction: # of decimal places = least number of decimal places of measurements

Examples

3.3 x 5820

17000

0.0

(3.60 x 10-3) x (8.123) / 4.3

0.0068

0.0

1.842 + 45.2 + 87.55

134.6

0.0

714.3-18.56

695.7

0.0