PERCENTSDefinitionA
percentage is a way of expressing a number as a fraction of 100 (
per cent meaning "per hundred"). It
is often denoted using the percent sign, "%", or the abbreviation "pct".
Since a percent is an amount per 100, percents can be represented as
fractions with a denominator of 100. For example, 25% means 25 per 100,
25/100 and 350% means 350 per 100, 350/100.
• A percent can be
represented as a decimal. The following relationship characterizes how
percents and decimals interact. Percent Form / 100 = Decimal Form
For
example: What is 2% represented as a decimal?
Percent Form / 100 =
Decimal Form: 2%/100=0.02
Percent changeGeneral
formula for percent increase or decrease, (percent change):
Example: A company received $2
million in royalties on the first $10 million in sales and then $8
million in royalties on the next $100 million in sales. By what percent
did the ratio of royalties to sales decrease from the first $10 million
in sales to the next $100 million in sales?
Solution: Percent decrease can be
calculated by the formula above:


,
so the royalties decreased by 60%.
Simple InterestSimple interest = principal * interest rate *
time, where
"principal"
is the starting amount and
"rate"
is the interest rate at which the money grows per a given period of
time (note: express the rate as a decimal in the formula). Time must be
expressed in the same units used for time in the Rate.
Example: If $15,000 is invested at 10%
simple annual interest, how much interest is earned after 9 months?
Solution: $15,000*0.1*9/12 = $1125
Compound Interest

,
where C = the number of times compounded annually.
If C=1,
meaning that interest is compounded once a year, then the formula will
be:


,
where time is number of years.
Example:
If $20,000 is invested at 12% annual interest, compounded quarterly,
what is the balance after 2 year?
Solution:

PercentileIf
someone's grade is in

percentile of the

grades, this means that

of
people out of

has the grades less than this person.
Example: Lena’s grade was in the 80th percentile out of
120 grades in her class. In another class of 200 students there were 24
grades higher than Lena’s. If nobody had Lena’s grade, then Lena was
what percentile of the two classes combined?
Solution:Being in 80th percentile
out of 120 grades means Lena outscored

classmates.
In another class she would outscored

students.
So, in combined classes she outscored

.
As there are total of

students, so Lena is in

, or in
85th percentile.
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