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Basic Math 2

What's next?

Decibels, Fractions, and measurement systems

Keep in mind that there are different ways to convey your information, and convert back and forth.

Example of ways to say the same thing:

1 dollar bill is same as 4 quarters.

1 dollar is equal to 4 quarters.

1 dollar = 4 quarters. 

4 quarters = 1 dollar.

1 quarter is worth 1/4 (quarter) of a dollar.

2 quarters are worth 1/2 (half) of a dollar.

3 quarters are worth 3/4 (three quarters) of a dollar.

1 quarter make 0.25 of a dollar.

2 quarters make 0.50 of a dollar.

3 quarters make 0.75 of a dollar

4 quarters make 1.0 dollar.

1 quarter is 25% of a dollar.

2 quarters is 50% of a dollar.

3 quarters is 75% of a dollar

4 quarters is 100% of a dollar.

Decibels and Fractions (Standard, Imperial)

Kids, go get a U.S. standard ruler or tape measure, we are going to use them for our examples.

Below, an inch on a tape measure is cut into 16 slices to measure in-between whole numbers. (But ultimately, it could be cut into any number of slices.)
ruler_edited.jpg
1 inch is same as 1.0 inch.
1/16 inch is same as 0.0625 inch.
1/8 = 0.125 inch
5/16 = 0.3125 inch
3/8 = 0.375 inch
7/16 = 0.4375 inch
1/2 = 0.500 inch
9/16 = 0.5625 inch
5/8 = 0.625 inch
11/16 = 0.6875 inch  
3/4 = 0.750 inch
13/16 = 0.8125 inch  
7/8 = 0.875 inch
15/16 = 0.9375 inch  
16/16 = 1.00000 inch
Same math applies to anything cut into 16 slices or segments, like the circle below (making a hexadecagon).

Decibels and Fractions (Metric)

Same as above, but using the metric system, and vice versa.

Kids, go get a metric ruler.

The metric system is based off 10's, so lets see work.

Below image has middle increment lines of 10, 20, 30, 40, 50 centimeters (cm). So, 10cm each.

Bottom increment lines are 1 millimeter (mm) each.

Top increment lines are 0.5 mm each.

That was a small example, lets review the metric system more.

4 main concepts:

1. Volume (Liter, L)

2. Mass (gram, g)

3. Length (meter, m)

4. Temperature (Celsius, C)

A Few Metric Unit Prefixes:

kilo - hecto - deca - (base unit) - deci - centi - milli

Different conversions of liters:

kl   → kiloliter     1000.0 x greater than the base unit.

hl   → hectoliter  100.0 x greater...

dal → decaliter   10.0 x greater...

l     → liter          1.0 x greater...

dl   → deciliter    0.1 x greater...

cl   → centiliter   00.1 x greater...

ml  → milliliter   000.1 x greater...

Which can get confusing when then thinking:

1L = 0.001 kL

1L = 0.01 hL

1L = 0.1 daL

1L = 1.0 L

1L = 0.1 dL

1L = 0.01 cL

1L = 0.001 mL

Common Metric Sizes:

Where else measurements used?

The metric system is used for very small and very large things!

For example:

Standard and Metric Conversions

Cookbook have the wrong units?! Convert!

tsp = teaspoon. tbsp = tablespoon. ml = milliliter. fl oz = fluid ounce.

oz = ounce. g = gram. C = Celsius. F = Fahrenheit.

Percent

Percent is described by using​ increments of 100 of something.

So, 1/100 is 1%.

1 of 100 is 1%.

100/100 is 100%.

50/100 = 50%.

50/50 = 1 = 100%

25/50 = 1/2 = 50%

500/1000 = 50/100 = 5/10 = 1/2 = 50%

Food for thought and more conversions ahead...

Time

24 hours in 1 day.

60 minutes in 1 hour.

60 seconds in 1 minute.

3600 seconds = 1 hour.

86400 seconds = 1 day.

6 hours is 6/24 of a day.

6/24 is same as 0.25.

0.25 = 1/4.

1/4 = 25%

Do you sleep more than 25% of the day away?

Astronomical System of Units

How do you measure distance in space?

Time

The astronomical unit of time is the day (D, d), defined as 86,400 seconds or 365.25 days (1 year on Earth), or one revolution around the sun. 

Mass

The astronomical unit of mass is the solar mass (M)  It is equal to the mass of the Sun (1 M), 1.9885×10^30 kg. The Sun is about 333,000x the mass of the Earth, 5.97237×10^24 kg (1.31668×10^25 lb)(3.0×10^−6 M).

The Earth mass (M) is the unit of mass equal to that of the Earth. So, 1 M = 3.0×10^−6 M.

Distance

The light-year (ly) is the distance traveled by light in a vacuum in 365.25 days (1 year), which comes to 63,241 au (about 9.46 × 10^12 km).

The astronomical unit (AU, au) of length is now defined as exactly 149,597,870,700 meters. It is approximately equal distance between the Earth and Sun.

The parsec (pc) is about 3.26 light-years or 206,000 AU. Parsec is not a simple straight line drawn from the observer, it is obtained by the use of parallax and trigonometry. A megaparsec (Mpc) is one million parsecs (about 3,260,000 ly). A gigaparsec (Gpc) is one billion parsecs (about 3.26 billion ly).

The lunar distance (LD) is the distance between Earth and its moon, 0.002569 au (384,402 km).

Volume

The volume of planets is measured with cubic kiloliters (kl^3). The Sun is 1.409 x 10^18 kl^3 and Earth is 1.08321 x 10^12 kl^3.

Sound

How loud is your TV, car, mom's yell? Can you measure noise?

The unit decibels (dB) are usually used to measure sound levels. 

The greater the volume of your TV, the greater the decibel levels can be recorded.

noise_edited.jpg

Real world examples:

More than 80dB and maybe you need hearing protection?!

Terms and Definitions

The only way to learn mathematics is to do mathematics.
 
- Paul Halmos

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