Precision, Accuracy and Significant Figures Notes

Today’s Objectives

Compare and contrast accuracy and precision.

Identify the purpose of significant figures. Multiply, divide and add and subtract using

significant figure rules.

Precision vs. Accuracy

Accuracy

Accuracy is how close something comes to an accepted standard.

Precision

Precision - how fine the divisions or segments are and how repeatable the results.

Accurate = Correct

Precision = Consistent

Ideally an instrument is both accurate and precise

Precision can add to accuracy if the instrument is calibrated correctly.Deduct if not

Example: Tare (zero) a scale

Significant Figures Purpose

Significant digits carry the precision of the instrument used.

Why do them?Consistency between peopleEnsures that the precision of the results only

reflect the precision of the least precise measuring tool

If a sprinter is measured to have completed a 100.0 m race in 11.71 seconds, what is his average speed?

Average speed = 8.53970965 m/s Can we really measure a sprinter’s speed

that precisely?

Other Options Include:

8.53970965 m/s 8.5397097 m/s 8.539710 m/s or

8.53971 (What is the difference?)

8.53971 m/s

8.5397 m/s 8.540 m/s or 8.54 m/s

(What is the difference?)

8.54 m/s 8.5 m/s 9 m/s Which would you

choose?

Candle with a mass of 14.143g 2.7 hours is the burn time.

14.143g/2.7 hrs = 5.238148148 g/hr

This number magically became more precise

One who makes a square’s side 5.1 cm x 5.1 cm is not confident that the square is exactly 26.013496870584764240556 cm2.

Nor would it be useful to say the square is 30 cm2

One has to be careful claiming a greater precision than what is justified

A good rule of thumbNo final answer should have any

more precision attached to it than the LOWEST precision found among the numbers being worked.

Another words… you answer should not have more digits than the original numbers calculated

Significant Figures Practice

Sig Fig – Rules

Nonzero numbers are always significant

1.2343876493

Sig Fig – Rules

All final zeros after the decimal point are significant

1.000000, 345.600

Sig Fig – Rules

Zeros between two other significant digits are always significant.

1.001, 234.01, 3.404040

Sig Fig – Rules

Zeros used solely as placeholders are not significant.

0.0002, 0.0231, 0.003040

Practice Time

How Many Sig Figs?

10010.980.00340.0480

How Many Sig Figs?

6.04903030004.030.00000010

Calculating With Sig Figs

Scientific Notation shows you how many sig. figs are in the number.

Ex.2.5x102 This is 2 sig. figs.

1.0000x10-23 This has 5 sig. figs.

Calculating With Sig Figs

Adding and Subtracting Sig. Figs.

RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places.Example: When we add

3.76 g + 14.83 g + 2.1 g = 20.69 g 20.7g

Calculating With Sig Figs Multiplying and Dividing with Sig. Figs.

RULE: When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits.Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm3We look to the original problem and check the number of significant digits in each of the original measurements: Our answer can only show 3 significant digits because that is the least number of significant digits in the original problem.5946.50525 shows 9 significant digits, we must round to the tens place in order to show only 3 significant digits. Our final answer becomes 5950 cm3.