Precision vs. AccuracyPrecision vs. AccuracyPrecision vs. AccuracyPrecision vs. Accuracy
There really is a differenceThere really is a difference
Precision • How close the measurements are
to each other• How many decimal places are in
the measurement.
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
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—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