Precision vs Accuracy There really is a difference
![Precision vs. Accuracy There really is a difference Precision vs. Accuracy There really is a difference](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-1.jpg)
![Accuracy • Accuracy is how close the measured value is to the true or Accuracy • Accuracy is how close the measured value is to the true or](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-2.jpg)
![Precision • How close the measurements are to each other • How many decimal Precision • How close the measurements are to each other • How many decimal](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-3.jpg)
![Precision or Accuracy? Precision or Accuracy?](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-4.jpg)
![Which measurement is most precise? • 0. 01 m • 0. 0053 m Which measurement is most precise? • 0. 01 m • 0. 0053 m](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-5.jpg)
![Significant Figures Where do I round the answer? How do I record this measurement? Significant Figures Where do I round the answer? How do I record this measurement?](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-6.jpg)
![Significant Figures • Significant figures are important to measurements • All nonzero digits are Significant Figures • Significant figures are important to measurements • All nonzero digits are](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-7.jpg)
![When Zeros are Sig Figs • Zeros are significant when they are between nonzero When Zeros are Sig Figs • Zeros are significant when they are between nonzero](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-8.jpg)
![When zeros are NOT sig figs • If the zeros come before a nonzero When zeros are NOT sig figs • If the zeros come before a nonzero](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-9.jpg)
![When Sig Figs are Infinite • All Conversion Factors and Counting numbers have INFINITE When Sig Figs are Infinite • All Conversion Factors and Counting numbers have INFINITE](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-10.jpg)
![Summary of Sig Figs • Nonzero digits are always significant • Zeros are significant Summary of Sig Figs • Nonzero digits are always significant • Zeros are significant](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-11.jpg)
![Sig Figs in Measurement How to record the correct measurement Sig Figs in Measurement How to record the correct measurement](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-12.jpg)
![Significant Figures • Read the correct number of significant figures Significant Figures • Read the correct number of significant figures](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-13.jpg)
![Measure the following using significant figures Measure the following using significant figures](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-14.jpg)
![Use Sig. Figs to find this measurement Use Sig. Figs to find this measurement](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-15.jpg)
![Use the correct number of sig. figs in this measurement Use the correct number of sig. figs in this measurement](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-16.jpg)
![What digit would be estimated in using this ruler? A. B. C. D. E. What digit would be estimated in using this ruler? A. B. C. D. E.](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-17.jpg)
![What decimal place is estimated when using this ruler? A. Ones B. Tenths C. What decimal place is estimated when using this ruler? A. Ones B. Tenths C.](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-18.jpg)
![Measure the width of the rectangle using the correct number of sig figs. A. Measure the width of the rectangle using the correct number of sig figs. A.](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-19.jpg)
![Measure the length of the rectangle using the correct number of sig figs. A. Measure the length of the rectangle using the correct number of sig figs. A.](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-20.jpg)
![How many sig figs should be in the correct measurement of the length of How many sig figs should be in the correct measurement of the length of](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-21.jpg)
![The width of this rectangle is 0. 90 cm. How many significant figures are The width of this rectangle is 0. 90 cm. How many significant figures are](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-22.jpg)
![QOD—Entrance Ticket What is the mass to the correct number of significant digits? QOD—Entrance Ticket What is the mass to the correct number of significant digits?](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-23.jpg)
![QOD—Record the mass on this balance to the correct number of significant digits and QOD—Record the mass on this balance to the correct number of significant digits and](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-24.jpg)
![Calculations with Significant Figures Multiplication and Division Addition and Subtraction Calculations with Significant Figures Multiplication and Division Addition and Subtraction](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-25.jpg)
![Multiplication and Division • When multiplying and dividing the answer is rounded to the Multiplication and Division • When multiplying and dividing the answer is rounded to the](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-26.jpg)
![Example 1 Ex. 9. 00 cm x 1, 000 cm = 9. 00 cm Example 1 Ex. 9. 00 cm x 1, 000 cm = 9. 00 cm](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-27.jpg)
![Example 2 Ex. 78. 0034 g / 80. 0 m. L = 78. 0034 Example 2 Ex. 78. 0034 g / 80. 0 m. L = 78. 0034](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-28.jpg)
![Example 3 Ex. 9. 70 x 104 m x 1. 76 x 10 -2 Example 3 Ex. 9. 70 x 104 m x 1. 76 x 10 -2](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-29.jpg)
![Addition and Subtraction with Sig Figs • The least number of decimal places in Addition and Subtraction with Sig Figs • The least number of decimal places in](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-30.jpg)
![Example 1 • 12. 573 m + 3847. 91 m – 378. 1 m Example 1 • 12. 573 m + 3847. 91 m – 378. 1 m](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-31.jpg)
![Try these in your notes 1. A rectangle has a width of 5. 00 Try these in your notes 1. A rectangle has a width of 5. 00](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-32.jpg)
![Answer • Calculator says 42 • But we need 3 sig figs and this Answer • Calculator says 42 • But we need 3 sig figs and this](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-33.jpg)
![Try this one in your notes 2. A triangle has the following measurements: side Try this one in your notes 2. A triangle has the following measurements: side](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-34.jpg)
![Answer • Calculator displays 26. 34 • We need only 1 decimal place, so Answer • Calculator displays 26. 34 • We need only 1 decimal place, so](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-35.jpg)
![Summary • Multiplication and Division use the least number of significant figures in the Summary • Multiplication and Division use the least number of significant figures in the](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-36.jpg)
- Slides: 36
![Precision vs Accuracy There really is a difference Precision vs. Accuracy There really is a difference](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-1.jpg)
Precision vs. Accuracy There really is a difference
![Accuracy Accuracy is how close the measured value is to the true or Accuracy • Accuracy is how close the measured value is to the true or](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-2.jpg)
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 Precision • How close the measurements are to each other • How many decimal](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-3.jpg)
Precision • How close the measurements are to each other • How many decimal places are in the measurement.
![Precision or Accuracy Precision or Accuracy?](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-4.jpg)
Precision or Accuracy?
![Which measurement is most precise 0 01 m 0 0053 m Which measurement is most precise? • 0. 01 m • 0. 0053 m](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-5.jpg)
Which measurement is most precise? • 0. 01 m • 0. 0053 m
![Significant Figures Where do I round the answer How do I record this measurement Significant Figures Where do I round the answer? How do I record this measurement?](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-6.jpg)
Significant Figures Where do I round the answer? How do I record this measurement?
![Significant Figures Significant figures are important to measurements All nonzero digits are Significant Figures • Significant figures are important to measurements • All nonzero digits are](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-7.jpg)
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 When Zeros are Sig Figs • Zeros are significant when they are between nonzero](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-8.jpg)
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 When zeros are NOT sig figs • If the zeros come before a nonzero](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-9.jpg)
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 g
![When Sig Figs are Infinite All Conversion Factors and Counting numbers have INFINITE When Sig Figs are Infinite • All Conversion Factors and Counting numbers have INFINITE](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-10.jpg)
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 Summary of Sig Figs • Nonzero digits are always significant • Zeros are significant](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-11.jpg)
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 Measurement How to record the correct measurement Sig Figs in Measurement How to record the correct measurement](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-12.jpg)
Sig Figs in Measurement How to record the correct measurement
![Significant Figures Read the correct number of significant figures Significant Figures • Read the correct number of significant figures](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-13.jpg)
Significant Figures • Read the correct number of significant figures
![Measure the following using significant figures Measure the following using significant figures](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-14.jpg)
Measure the following using significant figures
![Use Sig Figs to find this measurement Use Sig. Figs to find this measurement](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-15.jpg)
Use Sig. Figs to find this measurement
![Use the correct number of sig figs in this measurement Use the correct number of sig. figs in this measurement](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-16.jpg)
Use the correct number of sig. figs in this measurement
![What digit would be estimated in using this ruler A B C D E What digit would be estimated in using this ruler? A. B. C. D. E.](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-17.jpg)
What digit would be estimated in using this ruler? A. B. C. D. E. Ones Tenths Hundredths Thousandths Tens
![What decimal place is estimated when using this ruler A Ones B Tenths C What decimal place is estimated when using this ruler? A. Ones B. Tenths C.](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-18.jpg)
What decimal place is estimated when using this ruler? A. Ones B. Tenths C. Hundredths D. Thousandths E. Tens
![Measure the width of the rectangle using the correct number of sig figs A Measure the width of the rectangle using the correct number of sig figs. A.](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-19.jpg)
Measure the width of the rectangle using the correct number of sig figs. A. 3. 75 cm B. 3. 6 cm C. 2. 6 cm D. 3. 60 cm E. 4. 25 cm
![Measure the length of the rectangle using the correct number of sig figs A Measure the length of the rectangle using the correct number of sig figs. A.](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-20.jpg)
Measure the length of the rectangle using the correct number of sig figs. A. 12. 55 cm B. 12. 5 cm C. 12. 0 cm D. 13. 50 cm E. 13. 5 cm
![How many sig figs should be in the correct measurement of the length of How many sig figs should be in the correct measurement of the length of](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-21.jpg)
How many sig figs should be in the correct measurement of the length of this rectangle? A. 2 sig figs sig fig B. 3 sig figs C. 4 sig figs D. 5 sig figs E. 1
![The width of this rectangle is 0 90 cm How many significant figures are The width of this rectangle is 0. 90 cm. How many significant figures are](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-22.jpg)
The width of this rectangle is 0. 90 cm. How many significant figures are in this measurement? A. 3 sig figs B. 2 sig figs C. 1 sig fig D. infinite sig figs E. none of the above
![QODEntrance Ticket What is the mass to the correct number of significant digits QOD—Entrance Ticket What is the mass to the correct number of significant digits?](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-23.jpg)
QOD—Entrance Ticket What is the mass to the correct number of significant digits?
![QODRecord the mass on this balance to the correct number of significant digits and QOD—Record the mass on this balance to the correct number of significant digits and](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-24.jpg)
QOD—Record the mass on this balance to the correct number of significant digits and record the unit of measure.
![Calculations with Significant Figures Multiplication and Division Addition and Subtraction Calculations with Significant Figures Multiplication and Division Addition and Subtraction](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-25.jpg)
Calculations with Significant Figures Multiplication and Division Addition and Subtraction
![Multiplication and Division When multiplying and dividing the answer is rounded to the Multiplication and Division • When multiplying and dividing the answer is rounded to the](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-26.jpg)
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 1 Ex 9 00 cm x 1 000 cm 9 00 cm Example 1 Ex. 9. 00 cm x 1, 000 cm = 9. 00 cm](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-27.jpg)
Example 1 Ex. 9. 00 cm x 1, 000 cm = 9. 00 cm = ______ sig figs 9. 00 cm = 3 sig fig (decimal and 9) 1, 000 cm = _______ sig figs 1, 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 cm 2 (1 sig fig zeros are not significant; only a 9 but no decimal)
![Example 2 Ex 78 0034 g 80 0 m L 78 0034 Example 2 Ex. 78. 0034 g / 80. 0 m. L = 78. 0034](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-28.jpg)
Example 2 Ex. 78. 0034 g / 80. 0 m. L = 78. 0034 g = ____ sig figs 78. 0034 g = 6 sig figs (sandwich rule) 80. 0 m. L = ___ sig figs 80. 0 m. L = 3 sig fig (8 and decimal) Least number of sig figs? 3 sig figs so answer should have 3 sig figs Calculator answer = 0. 9750425 round to 3 sig figs 0. 975 g/m. L is the final, rounded answer
![Example 3 Ex 9 70 x 104 m x 1 76 x 10 2 Example 3 Ex. 9. 70 x 104 m x 1. 76 x 10 -2](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-29.jpg)
Example 3 Ex. 9. 70 x 104 m x 1. 76 x 10 -2 m 9. 70 x 104 m = ___ sig figs 9. 70 x 104 m = 3 sig figs (decimal and non zero digits) 1. 76 x 10 -2 m = ____ sig figs 1. 76 x 10 -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 m 2 Rounded to 3 sig figs may look like this 1710 m 2 or in scientific notation it would be 1. 71 x 103 m 3 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 Addition and Subtraction with Sig Figs • The least number of decimal places in](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-30.jpg)
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 Example 1 • 12. 573 m + 3847. 91 m – 378. 1 m](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-31.jpg)
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. 383 m (un-rounded) • 3482. 4 m (rounded)
![Try these in your notes 1 A rectangle has a width of 5 00 Try these in your notes 1. A rectangle has a width of 5. 00](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-32.jpg)
Try these in your notes 1. A rectangle has a width of 5. 00 cm and a length of 8. 40 cm. What is the area of this rectangle in cm 2? ______
![Answer Calculator says 42 But we need 3 sig figs and this Answer • Calculator says 42 • But we need 3 sig figs and this](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-33.jpg)
Answer • Calculator says 42 • But we need 3 sig figs and this is only 2. What should we do? • 42. 0 cm 2 or 4. 20 x 101 cm 2
![Try this one in your notes 2 A triangle has the following measurements side Try this one in your notes 2. A triangle has the following measurements: side](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-34.jpg)
Try this one in your notes 2. A triangle has the following measurements: side A 8. 54 cm, side B 7. 8 cm, and side C 10. 000 cm. What is the perimeter in cm? _______
![Answer Calculator displays 26 34 We need only 1 decimal place so Answer • Calculator displays 26. 34 • We need only 1 decimal place, so](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-35.jpg)
Answer • Calculator displays 26. 34 • We need only 1 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 Summary • Multiplication and Division use the least number of significant figures in the](https://slidetodoc.com/presentation_image_h/12bac3f9dda7595ee6bd4156caa9e0b2/image-36.jpg)
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
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