# Precision vs Accuracy There really is a difference

- Slides: 36

Precision vs. Accuracy There 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. 0053 m

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 • 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 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 Measurement How to record the correct measurement

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. B. C. D. E. Ones Tenths Hundredths Thousandths Tens

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. 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. 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 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 in this measurement? A. 3 sig figs B. 2 sig figs C. 1 sig fig D. infinite sig figs E. none of the above

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 Significant Figures Multiplication and Division Addition 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 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 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 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 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. 383 m (un-rounded) • 3482. 4 m (rounded)

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 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 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 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

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