Chapter One: Measurement

1.1 Measurements

1.2 Time and Distance

1.3 Converting Measurements

1.4 Working with Measurements

Section 1.4 Learning Goals

Determine the number of significant figures in measurements.

Distinguish accuracy, precision, and resolution.

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 2.56.

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 Experiment1. 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 thepaper 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 102

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 in2

FINAL ANSWER: # Sig. fig’s= 94 in2

For Final

Answer, y

ou

need to figure

out how m

any

sig fig’s!

Final answer: 4.3

Final answer: 242 or 2.42 X 102

Calculation Rules

Scientific Notation

Simply a method (short hand for numbers) for

expressing and working with really big OR really

small numbers.

See video