Using Scientific Measurements Chapter 2 section 3

Objectives 1. Distinguish between accuracy and precision. 2. Determine the number of significant figures in measurements. 3. Perform mathematical operations involving significant figures. 4. Convert measurements into scientific notation.

Accuracy and Precision Accuracy is the closeness of a measurement to the correct (accepted) value of quantity measured. Precision is a measure of how close a set of measurements are to one another. To evaluate the accuracy of a measurement, the measured value must be compared to the correct value. To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements

Accuracy vs Precision

Example: Accuracy Who is more accurate when measuring a book that has a true length of 17.0 cm? Susan: 17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm Amy: 15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

Example: Precision Who is more precise when measuring the same 17.0 cm book? Susan: 17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm Amy: 15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

Is it Accurate, Precise, Both or Neither? Known Density = 3.11 g/mL Test Results 3.77, 3.81, 3.76, 3.80 Precise, not accurate Test Results 3.01, 3.89, 3.50, 5.99 Neither Test Results 3.04, 3.20, 3.13, 3.07 Accurate, not precise Test Results 3.11, 3.12, 3.12, 3.10 Both

What are some reasons for accuracy or precision being off? Some error or uncertainty always exists in any measurement. skill of the measurer conditions of measurement measuring instruments

What are some reasons for accuracy or precision being off? Some rulers have more marks than others Which ruler is more accurate? Which ruler has more uncertainty?

How do we represent error? Error is the difference between the actual (or accepted) value and the experimental value Percent Error Percent Error = Experimental – Accepted x100 Accepted

Accuracy - Calculating % Error If a student measured the room width at 8.46 m and the accepted value was 9.45 m what was their accuracy? Using the formula: % error = (Experimental - Accepted)÷ Accepted x100

Accuracy - Calculating % Error Since Exp V = 8.46 m, AV = 9.45 m % Error = (8.46 m – 9.45 m) ÷ 9.45 m x 100 = [ -0.99 m ÷ 9.45 m ] x 100 = -0.105 x 100 %Error = -10.5 % Note that the meter unit cancels during the division & the unit is %. The (-) shows that Exp V was low The student was off by almost 11% & must remeasure Acceptable % error is within 5%

Acceptable error is +/- 5% Values from –5% up to 5% are acceptable Values less than –5% or greater than 5% must be remeasured remeasure -5% 5% remeasure

What is the student's percent error? Example Problem #1 What is the student's percent error? Working in the laboratory, a student finds the density of a piece of pure aluminum to be 2.85 g/cm3.  The accepted value for the density of aluminum is 2.699 g/cm3.

A student takes an object with an accepted mass of 200 A student takes an object with an accepted mass of 200.00 grams and masses it on his own balance.  He records the mass of the object as 196.5 g.   What is his percent error? Example Problem #2

How to Check a Measurement for Precision Significant Figures How to Check a Measurement for Precision

Significant Digits & Precision The precision of a measurement is the smallest possible unit that could be measured. Significant Figures (sf) are the numbers that result from a measurement. When a measurement is converted we need to make sure we know which digits are significant and keep them in our conversion All digits that are measured are significant

Significant Digits & Precision What is the length of the bar? How many digits are there in the measurement? All of these digits are significant There are 3 sF cm 1 2 3 4 Length of Bar = 3.23 cm

Significant Digits & Precision If we converted to that measurement of 3.23 cm to mm what would we get? Right! 32 300 mm How many digits in our converted number? Are they all significant digits (measured)? Which ones were measured, and which ones were added because we converted? If we know the significant digits, we can know the precision of our original measurement

Significant Figures & Precision What if we didn’t know the original measurement – such as 0.005670 hm. How would we know the precision of our measurement.

Counting Significant Figures Numbers 1-9 always count. 4895.2 has 5 sig figs Zeroes in front never count. 0.0005454 has 4 sig figs Zeroes after decimal point AND a # count. 0.0880 has 3 sig figs 28500 has 3 sig figs Zeros between sig digits count. 3050 has 3 sig fig 0.002001 has 4 sig fig

How many sig figs in: 3 2 4 1 5 5.05 1200 0.02020 0.0005 50 50.00 123.45 8090

2.3 Rounding Rules for rounding numbers: < 5, don’t round up. Don't change the magnitude of the number. what is magnitude? How big or small the number is. Like is it in the thousands? Hundreds? Tenths? Billions? If a number is in the thousands, when you round it must STILL be in the thousands.

Round these numbers off to 3 significant figures. 1.84 $7160 NOT 716. Seven thousand dollars is not the same as seven hundred dollars!!! (Magnitude) 0.00131 24,900 1) 1.8374 2) $7162.32 3) 0.00131154 4) 24,925

2.3 Adding and Subtracting Addition and subtraction: Your final answer must have the same decimal places as the fewest decimal places. (Your answer can only be as accurate as the weakest link) 13.5478 - 11.20 2.3478  Final answer = 2.35 Rounded to 2.35 since 11.20 has two decimal places Focus on Decimal Places

2.3 Multiplication and Division Your final answer has the same # sig dig as the LEAST sig dig. 3.546 x 1.4 = 4.9644 = 5.0 2 sig fig cause 1.4 is 2 sig fig Focus on Sig Fig