# UC notes

```Unit Conversions Notes
Part 1: Units and numbers
Numbers with units are important in science.
Units are a comparison to a standard measurement.
Examples of units:
Length or distance---meters, feet, centimeters, inches, miles, kilometers
time---seconds, minutes, hours, days, years
volume----gallons, quarts, liters, milliliters
massâ€”kilograms, grams, milligrams
weightâ€”pounds, oz, Newtons
speed---miles/hour, feet/second, kilometers/hour
When calculating with numbers and units, you must carry along the unit and do the same calculation on the
unit as the number. Sometimes units are cancelled during calculations.
Examples:
250 miles/ 5 hours = 50 mi/hr
60 N x 2.5 m = 150 N-m
125 g/cm3 x 100 cm3 = 12500 g
75 mi/ hr x 1.5 hr =
112.5 mi
375 lb /ft3 x 2 ft = 750 lb/ft2
Part 2: Unit Conversions
We can change from one unit to another by unit conversions. A list of conversion factors is needed.
Use a conversion factor like a fraction where the unit you want is on top (numerator) and the unit given in the
problem is on the bottom (denominator). WANT/GIVEN
Examples:
1. 79 inches to ft
1ft = 12 inches
The unit we want is ft, unit given is inches
79 in (1ft/12 in) = 6.6 ft
Multiply by the number in the numerator and divide by the number in the denominator
the inches on the original number cancel with the inches in the bottom of the conversion fraction.
2. 29 gallons to liters
1gal=3.8 L
29 gal (3.8 L/ 1 gal) = 110.2 L
3.
5,000 mi to ft
1 mi= 5280 ft
5000 mi ( 5280 ft/1 mi) = 26400000ft
4. 275 mL to L
1L = 1000ml
275 mL ( 1L/1000mL) = 0.275 L
Complex unit conversions(2 step)
Complex units have numerator and denominator
ex: mi/hr ft/sec g/cm3 lb/in2
Change 45 mi/hr to ft/sec
Step 1--change numerator unit: want/given
45 mi/hr ( 5280ft/1 mi) =237600ft/hr
Step 2---Change denominator unit: given/want
237600ft/hr ( 1hr/3600sec) =66ft/sec
```
Number theory

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Complex analysis

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