Chapter 2 - Mathematics

Question 1

7 Base Units

Answer 1

Second
Meter
Kilogram
Kelvin (K)
Mole (mol): amount of substance
Ampere (A): electric current
Candela (cd): luminous intensity

Question 2

Temperature
Fahrenheit –> Celsius
Celsius –> Kelvin

Answer 2

a) F=1.8(C) + 32

b) K=C + 273

Question 3

One L equals…

One mL equals…

Answer 3

a) 1 dm^3

b) 1 cm^3

Question 4

Density Formula

Answer 4

Mass/Volume

Remember
M
D V

Question 5

Scientific Notation

Answer 5

(Number between 1 and 10) x 10^

Question 6

Scientific Notation: Addition and Subtraction
Same exponents
Unlike exponents

Answer 6

a) Only add the coefficients
ex. (7.35 x 10^2) + (2.43 x 10^2)= 9.78 x 10^2
b) Make the exponents the same
ex. (2.643 x 10^18) + (7.8 x 10^16)
(2. 643 x 10^18) + (0.078 x 10^18)=2.721 x 10^18

Question 7

Scientific Notation: Multiplication and Division
Multiplication
Division

Answer 7

a) Multiply coefficients and add exponents]
ex. (2 x 10^3) x (3 x 10^2) = 6 x 10^5
b) Divide coefficients and subtract exponents
ex. (9 x 10^8) / (3 x 10^-4) = 3 x 10^12

Question 8

Dimensional Analysis

Answer 8

When you convert one unit to another using proportions

Question 9

Accuracy vs Precision

Answer 9

Accuracy: how close a measurement is to the actual value
Precision: how close a measurement is to other measurements

Question 10

Percent Error Equation

Answer 10

Percent Error = ([error]/accepted value) x 100

Question 11

Error Equation

Answer 11

error = experimental value - accepted value

Question 12

Metric System

Answer 12

G: giga
M: mega
k: kilo
h: hecto
da/D: deca
BASE UNIT
d: deci
c: centi
m: milli
u: micro
n: nano
p: pico

Question 13

Factor Label Method

Answer 13

When converting from one metric unit to another

ex. 55 mm x 1 m/1000mm = 0.055 m

Question 14

Significant Figures: Basic Rules

Answer 14

1. all digits 1-9
2. captive zeros: zeros between significant digits
3. trailing zeros: zeros right to significant digit, only significant if there is a decimal
   ex. 100 - 1 significant figure
   ex. 100.0 - 4 significant figures
   ex. 100. - 3 significant figures
4. zeros following a decimal significant figure
   ex. 0.00047 - 2 significant figures; 0.4700 - 4 significant figures

Conversions are not considered when determining significant figures

Question 15

Significant Figures: Rounding Rules

Answer 15

1. If a digit is to be removed, only look at the next digit to the right of the last significant figure
   ex. 4.4469 –> 4.4 (only look at 4.44 to determine)
2. In a series of calculations, carry extra digits through to the final result, and then round
   ex. 28.0 + 23.538 + 25.68 = 77.218 –> 77.2
3. If the digit to the right of the last significant figure is a 5 followed by 0 or no other #, look at the last significant figure: if it’s odd, round up; if it’s even, don’t round up
   ex. 2.5350 –> 2.54
   ex. 2.5250 –> 2.52

Question 16

Significant Figures: Multiplication and Division

Answer 16

Number of significant figures in the result is the same as that of the factor with the least number of significant figures

 ex. 4.36 x 1.4 = 6.384 --> 6.4
 ex. (6.88 x 10^2) x (1.5 x 10^5) = 10.32 x 10^7 --> 10.3 x 10
 ex. (9.00000 x 10^7) / (3.00 x 10^3) = 3 x 10^4 --> 3.00 x 10^4

Question 17

Independent and Dependent Variables

Answer 17

Independent plotted on x-axis

Dependent plotted on y-axis

Question 18

Rounding Numbers for Addition and Subtraction

Answer 18

Round to the lowest amount of decimal places

ex. 1.42 + 14.2= 15.62 –> 15.6

Question 19

What is the line used in a line graph called? Why is it called this?

Answer 19

Best-fit line

The line is drawn so that as many points are on it, but not all of them do

Question 20

How does slope show the relationship between the dependent and independent variables?

Answer 20

Positive: dependent variable increases with independent variable
Negative: dependent variable decreases as independent increases