MATH 150 – G
02/23/2009
MORE ON UNITS
Temperature Units: Fahrenheit, Celsius, and Kelvin
To convert from
Conversion in words
Conversion formula
Celsius to Fahrenheit
Multiply by 1.8 (or 9/5), then
add 32
F = 1.8C + 32
Fahrenheit to Celsius
Subtract 32, then divide by 1.8
(or multiply 5/9
!
C=
Celsius to Kelvin
Add 273.15
K = C + 273.15
Kelvin to Celsius
Subtract 273.15
!
F " 32
1.8
C = K " 273.15
!
Example: Average human body temperature is 98.6º.What is it in Celsius and Kelvin.?
!
Density:
Population density is given by the number of people per unit area.
Example: Manhattan Island has a population of about 1.5 million people living in an area of about 22
square miles. What is the population density? Express the density using the area in square kilometers.
Homework (additional)
Page 97 49,50, 55, 65, 67, 85
USES AND ABUSES OF PERCENTAGES
Percentages:
The words per cent means “per 100” or ”divided by 100”.
Examples:
100% =
3%=
1
What happens if we multiply a quantity by 100%?
Example 22.5 x 100%=
a) Converting a percentage to a common fraction
Replace % with division by 100 and simplify the fraction if necessary.
45%=
25%=
b) Converting a percentage to a decimal
Drop % symbol and move the decimal point two places to the left(that is, divide by 100)
33%=
15.5%=
c) Converting a decimal to a percentage
Move the decimal point two places to the right (that is, multiply by 100)
0.756=
0.057=
d) Converting a common fraction to a percentage
Convert first to decimal form, and then convert to percentage.
3
=
4
Using Percentages as Fractions:
!
Example: In a recent survey, 31% of 983 people said that they smoke. How many people smoke?
Using Percentage to Describe Change:
Percentages are often used to describe how a quantity changes with time.
As an example, suppose the population of town was 20,000 in 1980 and 25,000 in 1990.
- Absolute change in the population was 5,000 because the population increased by 5,000 people.
- Relative change in the populations was 25%, or 0.25 because the increase of 5000 people was
25% of the starting population of 20,000.
Calculating absolute or relative change always involves two numbers: a starting number, or reference
value, and a new value.
Absolute change = new value – reference value
relative change =
absolute change new value " reference value
=
reference value
reference value
2
!
The relative change above gives a fraction. To convert it to a percentage multiply by 100%
Examples:
a) During a 12-month period, AT&T’s stock tripled in price from $25 to $ 75. What are the
absolute and relative changes in the stock price?
b) World population was 2.6 billion in 1950 and 6.0 billion in 2000. Describe the absolute and
relative change in world population from 1950 to 2000.
c) Sasha bought a computer 4 years ago for $750. Today it is worth only $225. Describe the
absolute and relative change in the computer’s value.
Using Percentages for Comparisons:
Absolute difference = compared value – reference value
relative difference =
!
absolute difference compared value " reference value
=
reference value
reference value
Examples:
b) a) Suppose we want to compare the price of a $50,000 Mercedes to the price of a $40,000
Lexus.
How much more does the Mercedes cost than the Lexus? What is it in percentage?
How much less does the Lexus cost than the Mercedes? What is it in percentage?
3
c) In a recent year, the US made $12.1 billion in international arms sales and Russia made $5.8
billion in arms sales. Find the absolute and relative difference (as percentage) considering
Russia’s sales as reference.
Percentages: of versus more than (or less than)
Consider that a population quadruples in size from 150 to 600.
Using more than: The new population is 300% more than original population
Using of: The new population is 400% of the original population.
-
If the compared value is P% more than the reference value, it is (100+P)% of the reference
value.
If the compared value is P% less than the reference value, it is (100 - P)% of the reference
value.
Examples:
a) Alex earns 30% less than Bill, so Alex’s salary is ______% of Bill’s Salary.
b) Jane is 15% taller than Mary, so Jane’s height is ______% of Mary’s height.
Homework
Page 150:
21,27, 29, 31, 33, 55, 57, 59, 61, 62, 63, 64, 65, 67, 69, 70, 73, 75, 77, 79
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