CHAPTER 9 :

Motion – Physics

Intro to MEASUREMENTS

SIGNIFICANT FIGURES

SCIENTIFIC NOTATION

CALCULATIONS

ACCURACY AND PRECICION

ERRORS

REVIEW OF METRIC SYSTEM

Significant figures and

calculations

Significant figures in a measurement include all of the digits

that are known, plus one more

digit that is estimated.

Significant Figures •Any digit that is not zero is significant

2.234 kg 4 significant figures

•Zeros between non-zero digits are significant.

607 m 3 significant figures

• Leading zeros (to the left) are not significant.

0.07 L 1 significant figure.

0.00520 g 3 significant figures

Trailing ( to the right) only count if there is a

decimal in the number.

5.0 mg 2 significant figures.

50 mg 1 significant figure.

Two special situations have an

unlimited number of Significant figures:

1.. Counted items

a) 23 people, or 425 thumbtacks

2 Exactly defined quantities

b) 60 minutes = 1 hour

Practice #1

How many significant figures in the following?

1.0070 m

17.10 kg

100,890 L

3.29 x 103 s

0.0054 cm

3,200,000 mL

5 dogs

5 sig figs

4 sig figs

5 sig figs

3 sig figs

2 sig figs

2 sig figs

unlimitedThis is a

counted value

Rounding Calculated Answers

Decide how many significant figures are needed

Round to that many digits, counting from the left

Is the next digit less than 5? Drop it.

Next digit 5 or greater? Increase by 1

3.016 rounded to hundredths is 3.02

• 3.013 rounded to hundredths is 3.01

• 3.015 rounded to hundredths is 3.02

• 3.045 rounded to hundredths is 3.04

• 3.04501 rounded to hundredths is 3.05

M 761.50

14.334

10.44

10789

8024.50

203.514

762

14.3

10.4

10800

8020

204

Make the following have 3 sig figs:

Significant Figures Using

Addition and Subtraction

The answer should be rounded to the

same number of decimal places as the

least number of decimal places in the

problem. Examples:

4.8

-3.965

0.835 0.8

1 decimal places

3 decimal places

3 is the rounding number,

and drop every number

behind

1. 6.8 + 11.934 =18.734 18.7 (3 sig

figs)

2. 89.332 + 1.1 = 90.432 round off to 90.4

3. 3.70 -2.9133 = 0.7867

Examples………

Multiplication and Division Round the answer to the same number of

significant figures as the least number

of significant figures in the problem.

Scientific Notation

What is scientific Notation?

Scientific notation is a way of

expressing really big numbers or really

small numbers.

It is most often used in “scientific”

calculations where the analysis must be

very precise.

Why use scientific notation?

For very large and very small numbers,

these numbers can expressed in a more

concise form.

Numbers can be used in a computation

with far greater ease.

Scientific notation consists of

two parts:

A number between 1 and 10

A power of 10

N x 10x

Changing standard form to

scientific notation.

EXAMPLE

5 500 000

=

EXAMPLE #2

0.0075

=

Numbers less than 1

will have a negative

exponent.

EXAMPLE #3

CHANGE SCIENTIFIC NOTATION TO

STANDARD FORM

2.35 x 108

EXAMPLE #4

9 x 10-5

TRY THESE

Express in scientific notation

1) 421.96

2) 0.0421

3) 0.000 56

4) 467 000 000

To change standard form to

scientific notation…

Place the decimal point so that there is

one non-zero digit to the left of the

decimal point.

Count the number of decimal places the

decimal point has “moved” from the

original number. This will be the

exponent on the 10.

Continued…

If the original number was less than 1,

then the exponent is negative. If the

original number was greater than 1,

then the exponent is positive.

TRY THESE

Change to Standard Form

1) 4.21 x 105

2) 0.06 x 103

3) 5.73 x 10-4

4) 4.321 x 10-5

If you can’t round to the correct number of significant figures

using standard form…….try scientific notation!!

Not usually done – but can get out of a

sig. fig. bind!!

Metric Conversions Ladder Method

KILO

1000

Units

HECTO

100

Units

DEKA

10

UnitsDECI

0.1

Unit

CENTI

0.01

Unit

MILLI

0.001

Unit

Meter

s

Liters

Gram

s

Ladder Method

How do you use the “ladder” method?

1st – Determine your starting point.

2nd – Count the “jumps” to your ending

point.

3rd – Move the decimal the same number

of jumps in the same direction.

How to use Exponent Method

12

3

If getting bigger X 10# of jumps

If getting smaller ÷ 10# of jumps

1000 mg = _______ g 1 L = _______ mL 160 cm = _______ mm

14 km = _______ m 109 g = _______ kg 250 m = _______ km

Conversion Practice

Compare using <, >, or =.

56 cm 6 m 7 g 698 mg

Write the correct abbreviation for each metric unit.

1) Kilogram _____ 4) Milliliter _____ 7) Kilometer _____

2) Meter _____ 5) Millimeter _____ 8) Centimeter _____

3) Gram _____ 6) Liter _____ 9) Milligram _____

Try these conversions, using the ladder method.

10) 2000 mg = _______ g 15) 5 L = _______ mL 20) 16 cm = _______ mm

11) 104 km = _______ m 16) 198 g = _______ kg 21) 2500 m = _______ km

12) 480 cm = _____ m 17) 75 mL = _____ L 22) 65 g = _____ mg

13) 5.6 kg = _____ g 18) 50 cm = _____ m 23) 6.3 cm = _____ mm

14) 8 mm = _____ cm 19) 5.6 m = _____ cm 24) 120 mg = _____ g

Metric Conversion Challenge

Converting Units (Derived Units)

• Ex: Convert 100 km/hr to m/s

• A Conversion like this must be done using multiple

conversion factors! We need to convert hours into

minutes and then minutes into seconds; then convert

Km to m

Converting m\s to km\h

Area

Changing around formulas to solve for

certain values

Accuracy or Precision

• PrecisionReproducibility of results

Several measurements afford the same

results

Is a measure of exactness

• AccuracyHow close a result is to the “true” value

Is a measure of rightness

Types of Errors

Random errors- the same error does

not repeat every time.

• Blunders

• Human Error

Systematic Errors

– These are errors caused by the way in

which the experiment was conducted. In

other words, they are caused by flaws in

equipment or experimental.

Can be discovered and corrected.

Accuracy vs Precision

π Accuracy Precision

3 NO NO

7.18281828 NO YES

3.14 YES NO

3.1415926 YES YES

Examples:

You measure the mass of a ring three

times using the same balance and get

slightly different values: 12.74 g, 12.72 g,

12.75 g. ( random error )

The meter stick that is used for measuring,

has a millimetre worn off of the end

therefore when measuring an object all

measurements are off.

( systematic error )