CHM 110 - CHEMISTRY AND ISSUES IN THE ENVIRONMENT

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PERCENTAGE PROBLEMS

Percentage is a very common method for expressing concentrations, parts, or changes. Percentage is used all the time when referring to money, i.e. percent interest on savings or loans, percent sales tax, percent sales discounts, percent tips.

PERCENT means parts in a hundred.

Therefore, 30% means 30/100 or 0.30 expressed as a decimal;
5% means 5/100 or 0.05 as a decimal.
The fraction, 30/100 is converted to percentage by multiplying by 100: 30/100 x 100 = 30%.
A decimal, 0.05 is converted to percentage by also multiplying by 100; 0.05 x 100 = 5%.

The reverse process is used to convert percentage back to decimals.
15% is really the same as 15 divided by 100; 15/100 or 0.15.

In general the percentage of anything calculated by dividing out the fraction represented by the ratio of the "part" per "whole". The decimal obtained is converted to percentage by multiplying by 100 (move decimal point two places to the right).

Percentage = part/whole x 100 or

Percentage =	part	x 100
	whole

Example: If a dress or shirt selling for $40.00 has been discounted to $30.00, what is the percent discount?

Solution: First find the amount of discount: 40.00 - 30.00 = 10.00
Then find the percentage: 10.00 = part; 40.00 = whole

Percentage =	10.00 (part)	x 100	= 25 %
	40.00(whole)

Example: If a bottle of wine contains 710 ml of which a part is 85 ml
alcohol, what is the percentage alcohol present?

Solution:

Percentage =	85 ml (part)	x 100	= 12 %
	710 ml (whole)

Calculating the "part" or fraction in a percentage problem.

Another common type of percentage problem is to calculate the amount of the part if the percentage and whole amount are known. The procedure is the same as when you want to calculate the dollar amount for a discount, interest on savings or a loan, or a gratuity tip.

Example: If a $25.00 neck tie has been discounted 15 %, how many
dollars off is it?

Solution: Can you mentally do it in your head? Do you mechanically move
the decimal point two places to the left on 15% to give 0.15 and then multiply by 25.00?

Algebra Solution:

Percentage =	(part)	x 100	= 15 %
	$25 (whole)

Solve for the "part". First divide both sides by 100 to give 15/100 = 0.15

(part)	= 0.15
$25 (whole)

Next multiply both sides by $25 to give (part) = 0.15 x $25 = $3.75

Use the percent of gasoline (43%) to find the barrels of oil consumed as gasoline per capita per year. The barrels of oil per capita per year is 22.9

Algebra Solution:

Percentage =	(part)	x 100	= 43%
	22.9 barrels(whole)

Solve for the "part". First divide both sides by 100 to give 43/100 = 0.43

(part)	= 0.43
22.9 barrels (whole)

Next multiply both sides by 22.9 to give (part) = 0.43 x 22.9 = 9.85 barrels oil per person per year consumed as gasoline.