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# 8/30/13 - PowerPoint PPT Presentation

8/30/13. Today I will measure objects to the correct degree of certainty Warm Up - Describe a real life situation where you might use the scientific method. Don’t use one we’ve done in class!. Measurements and Math. College Prep Physics. Measurements.

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• Today I will measure objects to the correct degree of certainty

• Warm Up - Describe a real life situation where you might use the scientific method. Don’t use one we’ve done in class!

### Measurements and Math

College Prep Physics

• A measurement consists of a number and a unit.

• That boy is almost 7 tall.

Seven what??

That boy is almost 7 feet tall.

• Metric System

• SI units – base units

• Length - meter

• Mass– gram (kilogram)

• Volume - liter

• Time – second

• Temperature – Kelvin

• Metric System

• Derived units – made up of bases

• Area → a = l x w

Meter squared (m2)

• Volume → v = l x h x w

meter cubed (m3)

• Density  D=m/v

g/mL or g/cm3

• Uncertainty in measurement

• When measuring, estimate the measurement to one place past the last place on the instrument.

• For example, measuring length

• Precision

• Will give the same number over and over again

• Accuracy

• Will be close to the accepted value

• Dimensional Analysis – a technique of converting between units using identities.

• Identities – fractions of two equal values.

1m = 100 cm

1 m .

100 cm

100 cm

1m

or

1 gram = how many kilograms?

1 liter = how many gigaliters?

1 m = 100 cm

124 m = ? cm

100 cm

124 m

=12400 cm

x

1

m

• 1. Start with what you are given

• 2. Set up your identity. x ------

• 3. Whatever unit is on top goes on the bottom.

• 4. Plug in conversion factors

• 5. Unit cancel!

• Multiply by top… Divide by bottom.

• Answer should have same # of sig figs as given

1 m = 1 x 109 nm

24000 nm= ? m

1 m

24000 nm

=0.000024 m

x

nm

1 x 109

• 1. Start with what you are given

• 2. Set up your identity. x ------

• 3. Whatever unit is on top goes on the bottom.

• 4. Plug in conversion factors

• 5. Unit cancel!

• Multiply by top… Divide by bottom.

• Answer should have same # of sig figs as given

1 g = 0.001 kg

0.033 kg = ? dg

1 g = 10 dg

We don’t have a direct conversion between kg and dgv.

10 dg

1 g

0.033 kg

330 dg

=

x

x

0.001

kg

1

g

1 L = 1000 mL

593 mL = ? cL

1 L = 100 cL

Again, no direct conversion between mL and cL.

1 L

100 cL

593 mL

x

59.3 cL

=

x

1000

mL

1

L

• Complex (derived) units

• Example – miles/hour

• Follow the rules to cancel units.

• Whatever unit is on top, goes on the bottom

• *If the unit starts on the bottom, it must go on top!!

• If I am traveling at 60.0 m/s, how fast am I going in km/hr?

• Today I will use dimensional analysis to convert between metric and English systems and to convert complex units

• Warm Up –

• How many Gg in 19,500,000 dg?

3.2 km = ? mi

1 mi = 1.61 km

1 mi

3.2 km

=1.98757764 mi

=2.0 mi

x

1.61

km

• 1. Start with what you are given

• 2. Set up your identity. x ------

• 3. Whatever unit is on top goes on the bottom.

• 4. Plug in conversion factors

• 5. Unit cancel!

• Multiply by top… Divide by bottom.

• Answer should have same # of sig figs as given

1 ft = 12 in

116 ft= ? cm

1 in = 2.54 cm

We don’t have a direct conversion between ft and cm.

2.54 cm

12 in

116 ft

=3535.68 cm

x

x

1

ft

1

in

=3540 cm

A large fish tank can hold 100 gallons of water. How many kL is this?

1 gal = 3.78 L

1 L = 0.001 kL

0.001 kL

3.78 L

100 gal

= 0.378 kL

x

x

1

gal

1

L

= 0.4 kL

• A cake requires 3.0 tablespoons of sugar per gallon of mix. How many tablespoons per quart (tbs/qt) is this?

gal

3.0 tbs

1

x

= 0.75 tbs/qt

gal

4 qt