Units 101

Question 1

unit

Answer 1

a standard for measurement of physical qualities that has a clear definition based on something constant

Question 2

Categories of units:

Answer 2

Standard/Imperial or Metric/SI

Question 3

List the different parts of this measurement in SI.

Answer 3

12 - value
k - prefix (kilo = 10^3)
m - unit (physical quality)

Question 4

What digits are Significant?

Answer 4

1. All non-zero digits.
   (ex. 7000 m. - 1sf)
2. Zeros between other sf’s.
   (ex. 7001 m. - 4sfs)
3. Zeros at the beginning of a number are not significant.
   (ex. 000.7 m. - 1sf)
4. Zeros at the end of decimals are significant.
   (ex. 0.00700 m. - 3sf)

Question 5

significant figures (sf)

Answer 5

any digit in a measurement that represents useful information

Question 6

How to add and subtract with sf’s:

Answer 6

Result must be rounded to have as many decimal spaces as the input with the fewest number of decimal spaces
(ex. 70s+67.7s+74.4856s = 212.1856s = 212s)

Question 7

How to multiply and divide with sf’s:

Answer 7

The product must have as many sf’s as the input with the fewest number of sf’s
(ex. 2m2.5m1.05m = 5.25m^3 = 5m^3)

Question 8

conversion

Answer 8

a process of translating a measurement in one kind of unit to something equal but with a different unit

Question 9

conversion factor

Answer 9

a statement that 2 things are equal, written as a fraction where the top and bottom are equal

Question 10

5 conversion steps

Answer 10

1. Identify the unknown
2. Identify what you do know
3. Choose conversion factors (original unit to unit you want)
4. Multiply it out
5. Check answer (do the units cancel, does the answer make sense, does the answer’s number of significant figures match the number of significant figures given?)

Question 11

coordinate systems

Answer 11

a means of identifying the position of a thing in a space using numbers called coordinates

Question 12

Cartesian coordinates:

Answer 12

define a location relative to an origin using (x,y) which tells x-position and y-position

Question 13

Polar coordinates:

Answer 13

define a location relative to a reference point using (r,θ) when r is a distance and θ is a direction (angle)

Question 14

Cartesian - Polar

Answer 14

• draw a triangle with base x and height y
• get r (a^2 + b^2 = c^2)
• get θ (tanθ = (y/x); y = rsinθ)

Question 15

Polar - Cartesian

Answer 15

• get y (sinθ = (y/r); y = rsinθ
• get x (cosθ = (x/r); x = rcosθ)

Question 16

Types of error:

Answer 16

Systematic error - Consistent, repeatable errors associated with a flaw in the measurement system, such as a miscalculated instrument. This type of error shifts all measurements in the same direction.
Random error - Variability in measurements due to unpredictable factors, such as slight fluctuations in environmental conditions or measurements technique. These errors can cause measurements to scatter around the true value.