Base Units

• Metric System• -standard, used internationally(easy to

communicate through language barriers• -makes conversions simpler• -based on the number 10 & eliminates useless

memorization of numbers

• SI – System Internationale – revised metric system, main difference is change to kg since more common compared to grams

Common Base Units – units that can be measured or altered using prefixes

MEASUREMENT UNIT SYMBOL

Length meter m

Mass gram g

Time second sec

Temperature Kelvin K

Volume of a Liquid liter L

Common Derived Units – units that must be calculated using more than one measurement

MEASUREMENT UNIT SYMBOL

Volume of a solid cubic centimeters cm3

Density grams per cm3 or mL g/cm3 or g/mL

Unit 2Common Prefixes – added to base units to change their magnitude and make them more applicable.

PREFIX SYMBOL NUMERICAL MEANING

Pico p 1 × 10-12

Nano n 1 × 10-9

Micro µ 1 × 10-6

Milli m 1 × 10-3

Centi c 1 × 10-2

Deci d 1 × 10-1

Deca da 1 × 101

Hecto H 1 × 102

Kilo k 1 × 103

Mega M 1 × 106

Unit Conversions

ConvertingInches to centimeters

10.0 in

We start by writing down the number and the unit

ConvertingInches to centimeters

10.0 in

1 in

2.54 cm

Our conversion factor for this is 1 in = 2.54 cm.Since we want to convert to cm, it goes on the top.

ConvertingInches to centimeters

10.0 in

1 in

2.54 cm

Now we cancel and collect units. The inches cancel out, leaving us with cm –

the unit we are converting to.

ConvertingInches to centimeters

10.0 in

1 in

2.54 cm = 25.4 cm

Since the unit is correct, all that is left todo is the arithmetic...

The Answer

Even though we have two different numbersand two different units, they represent theexact same length. You can check this by looking at a ruler – find the 10 in mark anddirectly across at the cm side. What numberdo you find?

A more complex conversionkm to mhr s

In order to work a NSCI 110 homework problem, we need to convert kilometers per hour into meters per second. We can do both conversions at once using the same method as in the previous conversion.

80 km

hr

A more complex conversionkm to mhr s

Step 1 –Write down the number and theunit!

80 km

hr

1 hr

3600 s

A more complex conversionkm to mhr s

First we’ll convert time. Our conversion factor is1 hour = 3600 sec. Since we want hours to cancel out, we put it on the top.

80 km

hr

1 hr

3600 s

1000 m

1 km

A more complex conversionkm to mhr s

Next we convert our distance from kilometers to meters. The conversion factor is 1 km = 1000 m.Since we want to get rid of km, this time it goes on the bottom.

80 km

hr

1 hr

3600 s

1000 m

1 km=

A more complex conversionkm to mhr s

Now comes the important step – cancel and collect units.If you have chosen the correct conversion factors, you should only be left with the units you want to convert to.

ms

80 km

hr

1 hr

3600 s

1000 m

1 km=

80,000 m

3600 s

A more complex conversionkm to mhr s

Since the unit is correct, wecan now do the math – simplymultiply all the numbers on thetop and bottom, then divide thetwo.

80 km

hr

1 hr

3600 s

1000 m

1 km=

80,000 m

3600 s= 22 m

s

A more complex conversionkm to mhr s

The Answer!!

80 km/hr and 22 m/s are both velocities. A car that is

moving at a velocity of 80 km/hr is traveling the

exact same velocity as a car traveling at 22 m/s.

Unit 2• Scientific Notation - a mathematical way to shorten

how we write very large or very small numbers. We use exponents to show the power of 10 that we are using.

• A positive exponent means a large number.• A negative exponent means a small number.• Rules: Move the decimal point until you have one

integer before the decimal. If you move it to the left it is (+) to the right it is (-).

• Ex. 6023 - move decimal 3 places to left to make 6.023, now we have to add the power of 10 with the exponent 103, so our final answer is 6.023 x 103.

Unit 2• Ex. 2 .0000000345 , we move decimal to the right 8

spaces for 3.45 x 10-8.

• Calculations with Scientific Notation.

• Use your calculator! Learn how to punch numbers in. You will have an EE or EXP key on your calculator, you need to learn how to do this!

• Ex. 6.023 x 10 23 x 4.5 x 10 8 = ??• Answer is 2.71 x 1032

• The sooner you learn how to do this, the better.

Precision vs. Accuracy• Precision- getting the same results over and over

again

• Accuracy- getting the correct results over and over again

• “you can have precision without accuracy but you can’t have accuracy without precision”

• Percent error- tells you how close you are to the true value

% error = │actual- theoretical│ x 100

actual

Significant Figures

Physical Science

What is a significant figure?• There are 2 kinds of numbers:

– Exact: the amount of money in your account. Known with certainty.

What is a significant figure?- Approximate: weight, height—anything

MEASURED. No measurement is perfect.

– Always show every digit your are sure of and one more that we consider uncertain.

– Ex. 1.00 cm means we knew the 1 and the .0, but after that we had to estimate.

When to use Significant figures

• When a measurement is recorded only those digits that are dependable are written down.

When to use Significant figures

–If you measured the width of a paper with your ruler you might record 21.7cm.

To a mathematician 21.70, or 21.700 is the same.

But, to a scientist 21.7cm and 21.700 cm are NOT the same

• 21.700cm to a scientist means the measurement is accurate to within one thousandth of a cm.

But, to a scientist 21.7cm and 21.70cm are NOT the same

• If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.7cm.

How do I know how many Sig Figs?

• Rule: All digits are significant starting with the first non-zero digit on the left.

How do I know how many Sig Figs?

• Exception to rule: In whole numbers that end in zero, the zeros at the end are not significant.

How many sig figs?

• 7• 40• 0.5• 0.00003• 7 x 105

• 7,000,000

• 1• 1• 1• 1• 1• 1

How do I know how many Sig Figs?

• 2nd Exception to rule: If zeros are sandwiched between non-zero digits, the zeros become significant.

How do I know how many Sig Figs?

• 3rd Exception to rule: If zeros are at the end of a number that has a decimal, the zeros are significant.

How do I know how many Sig Figs?

• 3rd Exception to rule: These zeros are showing how accurate the measurement or calculation are.

How many sig figs here?

• 1.2• 2100• 56.76• 4.00• 0.0792• 7,083,000,000

• 2• 2• 4• 3• 3• 4

How many sig figs here?

• 3401• 2100• 2100.0• 5.00• 0.00412• 8,000,050,000

• 4• 2• 5• 3• 3• 6

What about calculations with sig figs?

• Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

Add/Subtract examples• 2.45cm + 1.2cm = 3.65cm,

• Round off to = 3.7cm

• 7.432cm + 2cm = 9.432 round to 9cm

Multiplication and Division

• Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

A couple of examples

• 56.78 cm x 2.45cm = 139.111 cm2

• Round to 139cm2

•75.8cm x 9.6cm = ?

Oreo Lab• Your group will be given a sample of regular

and double stuff Oreos.• Do not Eat them! (yet)• Scientifically prove, both by mass and by

volume whether or not the double stuff is actually a double stuff. V= ∏r2 x h

• Must have data and proof.• You will use a scale and a small protractor ruler

as your measuring devices. • Record everything in a chart and write your

conclusion. Good luck!

The End

Have Fun Measuring and Happy Calculating!

Dimensional Analysis Quiz

1. 75 mL =____dm3

2. 10 miles = ____ km

3. 500 mm =_____ cm

4. 500 mL =_____ L

5. 24 km/hr = _____ mi/hr

6. .45 kg/L = _____ g/mL