precision vs. accuracy there really is a difference

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Precision vs. Precision vs. Accuracy Accuracy There really is a There really is a difference difference

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Precision vs. AccuracyPrecision vs. AccuracyPrecision vs. AccuracyPrecision vs. Accuracy

There really is a differenceThere really is a difference

Accuracy• Accuracy is how close the

measured value is to the true or actual amount or answer.

Precision • How close the measurements are

to each other• How many decimal places are in

the measurement.

Precision or Accuracy?

Which measurement is most precise?

• 0.01 m• 0.005 m• 0.0053 m

Significant FiguresSignificant FiguresSignificant FiguresSignificant FiguresWhere do I round the answer? How do Where do I round the answer? How do

I record this measurement?I record this measurement?

Significant Figures• Significant figures are important to

measurements• All nonzero digits are significant• Ex. 852 cm has 3 sig figs

When Zeros are Sig Figs

• Zeros are significant when they are between nonzero digits (sandwich rule) ex. 700,001 g

• Zeros are significant when it comes after a decimal point and a nonzero digit. (Power of Two Rule)

• Ex. 1.00 cm

When zeros are NOT sig figs

• If the zeros come before a nonzero digit ex. 0.00007346 m

• If it is at the end of a number that does NOT have a decimal point

ex. 18,000,000 g

When Sig Figs are Infinite

• All Conversion Factors and Counting numbers have INFINITE significant figures

• Ex. 2.54 cm = 1 inch (both the 2.54 and the 1 are infinitely significant)

• Counted values contain infinite significant• Ex. You have 1 science book on your desk.

That 1 has infinite sig figs because it is known to have been counted not measured.

Summary of Sig Figs• Nonzero digits are always significant• Zeros are significant if they are

between two non zero digits or if there is BOTH a decimal and a nonzero digit in front of the zeros

• Zeros are NOT significant in other situations (just a decimal, after a number without a decimal)

Sig Figs in Sig Figs in MeasurementMeasurement

Sig Figs in Sig Figs in MeasurementMeasurement

How to record the correct How to record the correct measurementmeasurement

Significant Figures• Read the correct

number of significant figures

Measure the following using significant figures

Use Sig. Figs to find this measurement

Use the correct number of sig. figs in this

measurement

What digit would be estimated in using this

ruler?

A. OnesB. TenthsC. HundredthsD. ThousandthsE. Tens

What decimal place is estimated when using

this ruler?

A. Ones D. ThousandthsB. Tenths E. TensC. Hundredths

Measure the width of the rectangle using the

correct number of sig figs.

A. 3. 75 cm D. 3.60 cmB. 3.6 cm E. 4.25 cmC. 2. 6 cm

Measure the length of the rectangle using the

correct number of sig figs.

A. 12.55 cm C. 12.0 cmD. 13.50 cm

B. 12. 5 cm E. 13. 5 cm

How many sig figs should be in the correct measurement

of the length of this rectangle?

A. 2 sig figs C. 4 sig figs E. 1 sig figB. 3 sig figs D. 5 sig figs

The width of this rectangle is 0.90 cm. How many significant

figures are in this measurement?

A. 3 sig figs D. infinite sig figsB. 2 sig figs E. none of the aboveC. 1 sig fig

QOD—Entrance Ticket What is the mass to the correct number of significant digits?

QOD—Record the mass on this balance to the correct number of significant

digits and record the unit of measure.

Calculations with Calculations with Significant FiguresSignificant FiguresCalculations with Calculations with Significant FiguresSignificant Figures

Multiplication and DivisionMultiplication and DivisionAddition and SubtractionAddition and Subtraction

Multiplication and Division

• When multiplying and dividing the answer is rounded to the LEAST number of sig figs of the data used in the calculations

• Examples to follow

Example 1Ex. 9.00 cm x 1,000 cm = 9.00 cm = ______ sig figs9.00 cm = 3 sig fig (decimal and 9)1,000 cm = _______ sig figs1,000 cm = 1 sig fig (no decimal just a 1)Least number of sig figs?1 sig fig, so answer should have only one sig fig

as well. 9,000 cm2 (1 sig fig zeros are not significant;

only a 9 but no decimal)

Example 2 Ex. 78.0034 g / 80.0 mL = 78.0034 g = ____ sig figs78.0034 g = 6 sig figs (sandwich rule)80.0 mL = ___ sig figs80.0 mL = 3 sig fig (8 and decimal)Least number of sig figs? 3 sig figs so answer should have 3 sig figsCalculator answer = 0.9750425 round to 3 sig figs0.975 g/mL is the final, rounded answer

Example 3Ex. 9.70 x 104 m x 1.76 x10-2 m 9.70 x 104 m = ___ sig figs9.70 x 104 m = 3 sig figs (decimal and non

zero digits)1.76 x10-2 m = ____ sig figs1.76 x10-2 m = 3 sig figs (all non zero digits)Which is the least number of sig figs? Both are the same, so there will be 3 sig

figs in the answer.Calculator says = 1707.2 m2 Rounded to 3 sig figs may look like this

1710 m2 or in scientific notation it would be 1.71 x 103 m3

Either answer is acceptable unless the directions state the answer must be in scientific notation.

Addition and Subtraction with Sig Figs

• The least number of decimal places in the input is the same number of decimal places in the output (answer).

Example 1• 12.573 m + 3847.91 m – 378.1 m

= ?• What is the LEAST number of

decimal places? • One decimal place, so the answer

should have one decimal place• 3482.383m (un-rounded)• 3482.4 m (rounded)

Try these in your notes1. A rectangle has a width of 5.00

cm and a length of 8.40 cm. What is the area of this rectangle in cm2? ___________

Answer • Calculator says 42• But we need 3 sig figs and this is

only 2. What should we do?• 42.0 cm2 or 4.20 x 101 cm2

Try this one in your notes

2. A triangle has the following measurements: side A 8.54 cm, side B 7.8cm, and side C 10.000 cm. What is the perimeter in cm? ______________

Answer • Calculator displays 26.34• We need only1 decimal place, so

what should we do?• 26.3 cm Did you remember the

unit of measurement in your answer?

Summary• Multiplication and Division use the least

number of significant figures in the data to round to that number of sig figs in the answer.

• Addition and Subtraction use the least number of DECIMALS in the data to round to that number of DECIMALS in the answer

• Don’t forget your unit of measurement