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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

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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

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Unit 2

Common 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

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Unit

Conversions

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Converting

Inches to centimeters

10.0 in

We start by writing down the

number and the unit

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Converting

Inches 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.

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Converting

Inches 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.

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Converting

Inches to centimeters

10.0 in

1 in

2.54 cm

25.4 cm

Since the unit is correct,

all that is left to

do is the arithmetic...

The

Answer

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Even though we have two different numbers

and two different units, they represent the

exact same length. You can check this by

looking at a ruler – find the 10 in mark and

directly across at the cm side. What number

do you find?

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A more complex conversion

km to m

hr 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.

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80 km

A more complex conversion

km to m

hr s

Step 1 –

Write down the

number and the

unit!

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80 km

1 hr

3600 s

A more complex conversion

km to m

hr s

First we’ll convert time. Our conversion factor is

1 hour = 3600 sec. Since we want hours to cancel

out, we put it on the top.

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80 km

1 hr

3600 s

1000 m

1 km

A more complex conversion

km to m

hr 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.

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80 km

1 hr

3600 s

1000 m

1 km

A more complex conversion

km to m

hr 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.

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80 km

1 hr

3600 s

1000 m

1 km

80,000 m

3600 s

A more complex conversion

km to m

hr s

Since the unit is correct, we

can now do the math – simply

multiply all the numbers on the

top and bottom, then divide the

two.

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80 km

1 hr

3600 s

1000 m

1 km

80,000 m

3600 s

A more complex conversion

km to m

hr s

The

Answer!!

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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.

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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.

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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.

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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

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Significant Figures

Physical Science

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What is a significant figure?

There are 2 kinds of numbers:

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

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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.

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When to use Significant figures

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

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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.

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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.

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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.

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