Measurements and Their Uncertainty 3.1

Measurements and Their Uncertainty 3.1 3.1

3.1 Significant Figures in Calculations • Significant Figures in Calculations • How does the precision of a calculated answer compare to the precision of the measurements used to obtain it?

3.1 Significant Figures in Calculations • In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated. • The calculated value must be rounded to make it consistent with the measurements from which it was calculated.

3.1 Significant Figures in Calculations • Rounding • To round a number, you must first decide how many significant figures your answer should have. The answer depends on the given measurements and on the mathematical process used to arrive at the answer.

3.1

for Sample Problem 3.1 Write down your answers. .

3.1 Significant Figures in Calculations • Addition and Subtraction • The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.

3.2

12.52 • 349.0 • 8.24 • 369.76 • Final Answer 369.8 meters

for Sample Problem 3.2 Write down your answers and round to The correct number of SF’s..

3.1 Significant Figures in Calculations • Multiplication and Division • In calculations involving multiplication and division, you need to round the answer to the same number of significant figures as the measurement with the least number of significant figures. • The position of the decimal point has nothing to do with the rounding process when multiplying and dividing measurements.

3.3

for Sample Problem 3.3 Write down your answer with the correct Number of SF’s.

Section Assessment • 3.1. Write down your answers.

3.1 Section Quiz • 1. In which of the following expressions is the number on the left NOT equal to the number on the right? • 0.00456  10–8 = 4.56  10–11 • 454  10–8 = 4.54  10–6 • 842.6  104 = 8.426  106 • 0.00452  106 = 4.52  109

3.1 Section Quiz • 2. Which set of measurements of a 2.00-g standard is the most precise? • 2.00 g, 2.01 g, 1.98 g • 2.10 g, 2.00 g, 2.20 g • 2.02 g, 2.03 g, 2.04 g • 1.50 g, 2.00 g, 2.50 g

3.1 Section Quiz • 3. A student reports the volume of a liquid as 0.0130 L. How many significant figures are in this measurement? • 2 • 3 • 4 • 5

END OF SHOW

Measurements and Their Uncertainty 3.1