Measurements in Experiments1.2 pp 10-19

Mr. Richter

Agenda

Turn in Posters

Warm-Up

Discuss Energy Paragraphs

Finish Yesterday’s Notes

Questions about the Quiz?

Introduction to the Metric System

Notes (Day 1): Measurement The Metric System (SI) Metric Prefixes and

Scientific Notation

Day 2: Accuracy Precision Significant Figures

Objectives: We Will Be Able To…

List basic SI units and the quantities they describe.

Convert measurements into scientific notation.

Distinguish between accuracy and precision.

Use significant figures in measurements and calculations.

Warm-Up:

There are 5280 feet in a mile. There are 1000 meters in a kilometer.

How many feet are in 4 miles?

How many meters are in 4 kilometers?

For Tomorrow’s Quiz You Should:

Review your notes

Review the slides online

Pay special attention to things I have repeated (Like vocab, objectives, homework problems…)

Bring a sharpened pencil and be ready to go at the bell tomorrow

Measurement

What are Measurements?

Measurements tell us how much of what kind of stuff we have.

Measurements require two things: A quantity – how much A dimension (units) – what kind

UNITS MATTER! My amount of wealth differs greatly if I have 30 million

dollars or 30 million yen I can’t say “I live four away from here.” It only makes

sense if I say “four miles” or “four kilometers”.

Système Internationale (SI) aka The Metric System

All scientists and most countries use the SI or metric system.

Why? Because it is easy to convert between large and small units. And to use scientific notation.

The SI system has three base units (p. 11): Meter – length Kilogram – mass Second – time

All other units are combinations or derivations of these three.

Metric Prefixes

The SI uses metric prefixes and scientific notation to accommodate extreme values of the base units.

You will be required to memorize: nano- micro- milli centi kilo- mega-

Homework for Tonight

p14 #1-5

Warm-Up

Work by yourself in your notes to answer each question.

Remember to think in terms of being realistic: are meters larger or smaller than the original unit?

If you can, try to do this from memory; without the prefix charts.

How many meters is:

1. 42 kilometers

2. 4.2 kilometers

3. 0.42 kilometers

4. 4200 centimeters

5. 420 centimeters

6. 42 centimeters

7. 4.2 centimeters

Agenda

Warm-Up

Review Quiz

Set Up Portfolios

Review Homework

More On Metric Conversions

Scientific Notation

Accuracy and Precision

Significant Figures

Objectives: We Will Be Able To…

List basic SI units and the quantities they describe.

Convert measurements into scientific notation.

Distinguish between accuracy and precision.

Use significant figures in measurements and calculations.

Converting with Metric Prefixes (Another Method)

1 mm = 10-3 m, therefore:

To convert between units, multiply by the conversion factor.

Make sure units cancel out.

Bad:

Good:

Using Units

Units must agree. A fancy way of saying that the units used to express a measurement must match.

For example: Don’t use kilograms to measure

length. Duh. Sometimes people will use different

units of distance to measure the same thing, like area. Avoid and convert: feet-meters centimeter-meters

Scientific NotationReview

Scientific Notation

Used in conjunction with metric prefixes to indicate the size of a measurement.

To convert to scientific notation: slide decimal point to the right of the first non-zero value

0.000345 3.45 267000 2.67000

then multiply by a power of 10 to compensate for the shifted decimal point 0.000345 3.45 x 10-4

267000 2.67000 x 105

Your Turn

Convert the following values into scientific notation:

1. 4200

2. 340.6

3. 0.02

4. 0.00650

How did you do?

1. 4.2 x 103

2. 3.406 x 102

3. 2 x 10-2

4. 6.50 x 10-3

Warm-Up

Express the following measurements in scientific notation: 346 meters 2400 grams 0.0018 meters/second

How did you do? 3.46 x 102 m 2.4 (or 2.40 or 2.400) x 103 g 1.8 x 10-3 m/s

Scientific Notation

The real reason for scientific notation: not just because we’re sick of writing zeros. Scientific notation allows us to compare the sizes of

numbers almost instantaneously.

Which number is bigger? 23000000000000000 or 170000000000000000

How much easier is it in scientific notation? 2.3 x 1016 or 1.7 x 1017

Accuracy and Precision

Accuracy

Describes how close a measured value is to the true value of the quantity measured.

Errors in accuracy come from: human error – incorrect use of instrument or

science using a tape measure incorrectly reading a thermometer at the wrong level

instrument error – the device used to take a measurement doesn’t work the tape measure or thermometer is

broken

Precision

Refers to the degree of exactness with which a measurement is made and stated.

Errors in precision come from the limitations of an instrument, not human error or calibration.

For example: if the scale at the doctor’s office measures only to the nearest kilogram, then the doctor cannot be expected to state your mass to the nearest tenth of a kilogram.

Accuracy vs. Precision: Length

The length of a 18-cm pencil is measured three times with a ruler by three different people:

The length is measured to be about 18 cm each time: accurate but not precise.

The length is measured to be 16.92 cm, 20.31 cm, and 17.75 cm respectively: precise but not accurate.

The length is measured to be 17. 98 cm, 18.03 cm, and 17.96 cm: both accurate and precise.

Significant FiguresWhat numbers matter? (Summary of rules pp. 17-19)

Significant Figures (SigFigs)

Significant figures indicate the degree of precision with which a measurement was taken.

For example: 23 meters vs. 23.0 meters. What’s the difference? The same number mathematically, but the latter is more

precise. The measurement was taken with a more precise instrument.

Significant Figures comes down to: Which zeros don’t matter? Any in front of non-zero digits: 0.0008 Any at the end of a number but to the left of the decimal: 2000

Significant Figures and Scientific Notation

Scientific notation tells the difference between significant and insignificant figures.

For example: 200 could have 1 significant figure or 3.

In scientific notation: 200 = 2 x 102, or 200 = 2.00 x 102

It is easy to see which measurement is more precise written in scientific notation.

Calculations with Significant Figures

Adding: the sum should have the same number of digits to the right of the decimal as the least precise measurement. 250.4 + 112 ≠ 362.4 (indicates too much precision) 250.4 + 112 = 362

Multiplying: the product should have the same number of significant figures as the least precise measurement. 4.6 x 6.7 ≠ 30.82 (indicates too much precision) 4.6 x 6.7 = 31

Note: Your calculator doesn’t get sig figs.

Your Turn

Try p. 28 #20, a-d

Wrap-Up: Did we meet our objectives?

List basic SI units and the quantities they describe.

Convert measurements into scientific notation.

Distinguish between accuracy and precision.

Use significant figures in measurements and calculations.

Homework

Due Wed:

p19 #1-4