Base Units

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# Base Units - PowerPoint PPT Presentation

Base Units. Metric System -standard, used internationally(easy to communicate through language barriers -makes conversions simpler -based on the number 10 &amp; eliminates useless memorization of numbers

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Presentation Transcript

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

### Unit 2

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

Unit

Conversions

Converting

Inches to centimeters

10.0 in

We start by writing down the

number and the unit

Converting

Inches to centimeters

10.0 in

2.54 cm

1 in

Our conversion factor for this is 1 in = 2.54 cm.

Since we want to convert to cm, it goes on the

top.

Converting

Inches to centimeters

10.0 in

2.54 cm

1 in

Now we cancel and collect units. The inches cancel

out, leaving us with cm –

the unit we are converting to.

Converting

Inches to centimeters

10.0 in

2.54 cm

25.4 cm

=

1 in

Since the unit is correct,

all that is left to

do is the arithmetic...

The

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?

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.

A more complex conversion

km to m

hr s

Step 1 –

Write down the

number and the

unit!

80 km

hr

A more complex conversion

km to m

hr s

80 km

1 hr

hr

3600 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.

A more complex conversion

km to m

hr s

80 km

1 hr

1000 m

hr

3600 s

1 km

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.

A more complex conversion

km to m

hr s

80 km

1 hr

1000 m

m

=

s

hr

3600 s

1 km

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.

A more complex conversion

km to m

hr s

80 km

1 hr

1000 m

=

hr

3600 s

1 km

80,000 m

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.

3600 s

A more complex conversion

km to m

hr s

80 km

1 hr

1000 m

=

hr

3600 s

1 km

80,000 m

m

22

The

=

s

3600 s

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.
7

40

0.5

0.00003

7 x 105

7,000,000

1

1

1

1

1

1

How many sig figs?
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.
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

How many sig figs here?
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.
• 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