“Uncertainty in Measurement”

• A measurement always involves a comparison ofknown vs. unknown

• Exact numbers have values that are known exactly (given from a textbook)

• Inexact numbers have values that include some level of uncertainty (measurements)

Linked

“Precision & Accuracy”

Precision -

Accuracy -

Linked

Different measuring tools may have differing levels of

certainty

Significant Figures

• All digits of a measured quantity, including the uncertain one, are called significant

“If you measured it (even though you may be uncertain) it is significant or meaningful to you!”

Counting Significant Figs

1) All nonzero digits are significant.

2) Zeros in-between significant figures are significant.

3) Zeros beyond the decimal point at the end of a number are significant.

4) Zeros preceding the first significant figures in a number are NOT significant.

Counting Significant Figures

• How many sig figures do the following #s have?

23.2 cm 0.0250 g

50.00 mL 1000 s

8.07840 g 0.03289700 g

• If a calculator displays 12.846239 and only 3 significant figures are justified, what would you round to?

• Beware of “Place-Holder Zeros” !!!

Round off 151.1 to 2 sig figs?

Round off 14652.83 to 3 sig figs?

Rounding Off Nonsignificant Figs

Rounding Off Nonsignificant Figures1. If the first nonsignificant figure is less

that 5, drop all nonsignificant figure

2. If the first nonsignificant figure is ≥5, increase the last significant figure by 1 and drop all nonsignificant figures.

3. If a calculation has 2 or more operations, retain the nonsignificant figures until the final operation.

Calculations using Sig Figs

Addition/Subtraction

• The result must have the same number of decimal places as there are in the measured quantity with the smallest number of decimal places

(the answer is limited by the measured value with the most uncertainty)

12 g + 12.1 g + 12.01g = 36.11gapply the rule and round and the answer is 36 g

Adding/Subtracting Sig Figs

• 8.6 cm + 50.05 cm =

• 2.6817 – 0.467 =

• 2.1745 + 134.2 + 56.17 + 18.193 =

• 652.137 – 21.1 =

Calculations of Measurements

Multiplication/Division• The result must have the same number of

significant figures as there are in the measured quantity with the smallest number of significant figures

(867.5309 mg) / (9.0210mL)=163.08181mg/mL

apply the rule and round and the answer is 163.08mg/mL

Multiplying and Dividing Sig Figs

(134.75)(25.83)(3.23) =

(4534.111) ÷ 124.73) =

(95.86)(2.117)(15.3)(874.11)(11.312)(77.22)

=