Chapter One: Measurement 11.1 Measurements 11.2 Time and Distance 11.3 Converting Measurements 11.4 Working with Measurements

Section 1.4 Learning Goals DDetermine the number of significant figures in measurements. DDistinguish accuracy, precision, and resolution. CCompare data sets to determine if they are significantly different.

Accuracy vs. Precision  Accuracy is how close a measurement is to the accepted, true value.  Precision describes how close together repeated measurements or events are to one another.

Resolution  Resolution refers to the smallest interval that can be measured.  You can think of resolution as the “sharpness” OR “greatest number of divisions” of a measurement. Since clock has minute marks, resolution is 0.5 min. Graduated cylinder: 0.5 ml

Significant Differences  In everyday conversation, “same” means two numbers that are the same exactly, like 2.56 and  When comparing scientific results “same” means “not significantly different”.  Significant differences are differences that are MUCH larger than the estimated error in the results.

Dropping Ball Experiment 1. Use stop watch to time how long the ball is in the air. 2. Repeat two more times. 3. Are all three times EXACTLY the same? 4. What is same? Different? 5. Average your trials. 6. Is average same as everybody else? 7. What is same? Different?

What is the REAL answer?  In the real world it is impossible for everyone to arrive at the exact same true measurement as everyone else. What is the length of the paper clip in centimeters? 2.63 cm How many digits/decimal places are enough?

Digits that are always significant: 1.Non-zero digits (9 cm has one sig fig). 2.Zeroes between two significant digits (902 cm has three sig fig’s). 3.All final zeroes to the right of a decimal point (902.0 cm has four sig fig’s). Digits that are never significant: 4.Leading zeroes to the right of a decimal point. (0.009 cm has only one significant digit.) 5.Final zeroes in a number that does not have a decimal point (900 cm has one sig fig).

How many digits are significant?

Final answer: 4.3 Final answer: 242 or 2.42 X 10 2 Calculation Rules

Solving Problems What is area of 8.5 in. x 11.0 in. paper? 1.Looking for:  …area of the paper 2.Given:  … width = 8.5 in; length = 11.0 in 3.Relationship:  Area = W x L 4.Solution:  8.5 in x 11.0 in = 93.5 in 2 FINAL ANSWER: # Sig. fig’s= 94 in 2 For Final Answer, you need to figure out how many sig fig’s!

Final answer: 4.3 Final answer: 242 or 2.42 X 10 2 Calculation Rules

Scientific Notation Simply a method (short hand for numbers) for expressing and working with really big OR really small numbers.

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