Percents

% is a multiplier.


Basics
% = pct = percent

% = fraction of 100
1% = \bf\displaystyle\frac{1}{100}

5% = \bf\displaystyle\frac{5}{100}

23% = \bf\displaystyle\frac{23}{100}

There is an invisible decimal point between the number and %.
1% = 1.%
5% = 5.%
23% = 23.%

To convert percent to a decimal, move the invisible decimal point two places to the left; this maneuver is the same as dividing the percent by 100.
0.07 ← 7.% = 7%
7 ÷ 100 = 0.07
0.70 ← 70.% = 70%
70 ÷ 100 = 0.70

To convert a decimal to percent, move the decimal point two places to the right;
this maneuver is the same as multiplying the decimal by 100.
0.07 → 7.% = 7%
0.07 × 100 = 7%
0.70 → 70.% = 70%
0.70 × 100 = 70%

% is a multiplier.
The word of is a multiplier.
3% of 500 = 3% × 500

2nd % is the % command.
2nd 
activates % above ( .


Question
Convert 6% to a decimal.

Answer
0.06

Answer Process
To convert percent to a decimal, move the invisible decimal point two places to the left.
0.06 ← 6.% = 6%


Question
Convert 65% to a decimal.

Answer
0.65

Answer Process
To convert percent to a decimal, move the invisible decimal point two places to the left.
0.65 ← 65.% = 65%


Question
Convert 0.08 to percent.

Answer
8%

Answer Process
To convert a decimal to percent, move the decimal point two places to the right.
0.08 → 8.% = 8%


Question
Convert 0.85 to percent.

Answer
85%

Answer Process
To convert a decimal to percent, move the decimal point two places to the right.
0.85 → 85.% = 85%


Question
Bob earns 3% interest a year on his savings account.  If he starts the year with $50000 and does not withdraw anything from his savings account, how much interest will Bob earn by the end of the year?

Answer
$1500

Answer Process
% is a multiplier.
3% × 50000 = 1500

Calculator Click What You See Comment
clear blinker clears screen
2nd % × 50000 3%*50000 % is a multiplier.
enter 1500 Answer
Percent


Question
Bob earns 3% interest a year on his savings account.  If he starts the year with $50000 and does not withdraw anything from his savings account, what will Bob’s new balance be at the end of the year?

Answer
$51500

Answer Process
New Balance = Old Balance + Interest
New Balance = 50000 + 3% × 50000 = 51500

Calculator Click What You See Comment
clear blinker clears screen
50000 + 3 2nd % × 50000 50000+3%*50000
enter 51500 Answer
Percent


Question
Bob earns 3% interest a year on his savings account.  The bank imposes a $7.25 fee to withdraw all funds from such an account.  If Bob starts the year with $50000 in his savings account and withdraws everything at year-end, how much money will he have?

Answer
$51492.75

Answer Process
New Balance = Old Balance + Interest – Fee
New Balance = 50000 + 3% × 50000 – 7.25 = 51492.75

Calculator Click What You See Comment
clear blinker clears screen
50000 +
3 2nd % × 50000
– 7.25
50000+3%*50000-7.25
enter 51492.75 Answer
Percent


Question

The cost of Biff’s lunch at a sub shop before the sales tax was $6.50.  If the sales tax rate was 8%, how much did Biff owe for the sales tax?

Answer
$0.52

Answer Process
% is a multiplier.
8% × 6.50 = 0.52

Calculator Click What You See Comment
clear blinker clears screen
2nd % × 6.50 8%*6.50 % is a multiplier.
enter 0.52 Answer
Percent


Question
The cost of Biff’s lunch at a sub shop before the sales tax was $6.50.  If the sales tax rate was 8%, how much change did Biff receive after paying for his lunch with a ten-dollar bill?

Answer
$2.98

Answer Process
Change = Payment – Cost – Tax
Change = 10.00 – 6.50 – 8% × 6.50 = 2.98

Calculator Click What You See Comment
clear blinker clears screen
10.00 – 6.50 – 2nd % × 6.50 10.00-6.50-8%*6.50
enter 2.98 Answer
Percent


Question

The cost of Biff’s lunch at a sub shop before the sales tax was $6.50.  After an 8% sales tax was imposed, the cashier gave Biff change from a ten-dollar bill.  After receiving the change, Biff took four cents from the cashier’s penny dish.  If the ten-dollar bill was all the money Biff had before he entered the restaurant, how much money did Biff have after leaving the restaurant?

Answer
$3.02

Answer Process
10.00 – 6.50 – 8% × 6.50 + 0.04 = 3.02

Calculator Click What You See Comment
clear blinker clears screen
10.00 – 6.50 –
2nd % × 6.50
+ 0.04
10.00-6.50-8%*6.50+0.04
enter 3.02 Answer
Percent


Practice – Questions
1.  Convert 9% to a decimal.

2.  Convert 95% to a decimal.

3.  Convert 0.04 to percent.

4.  Convert 0.45 to percent.

5.  Convert 0.455 to percent.

6.  Betty, a real estate agent, earned a 6% commission on the sale of a $215000 house.
How much did Betty earn?

7.  With reference to Question 1, if, in a particular year, Betty sells only the $215000 house and earns $5000 answering the office phone on the side, how much did she earn that particular year?

8.  A new car costing $27500 depreciates (loses value) by 20% after one year?  By how much does the car depreciate after one year?

9.  With reference to Question 8, how much is the car worth after one year?

10.  Joe’s knee surgery cost $20000.  Because the health insurance company requires a deductible, Joe must pay the first $4000 out-of-pocket.  Because the health insurance company also requires a copayment, it will pay only 80% of the remaining balance.  How much of the remaining balance will the health insurance company pay?

11.  With reference to Question 10, how much of the remaining balance does Joe owe as the copayment?

12.  With reference to Questions 10 and 11, how much in total, including both the deductible and copayment, does Joe owe?

13.  A rare painting by a famous artist appreciates (increases value) by 15% a year.  If the initial value of the painting is $175000, by how much does it appreciate after one year?

14.  With reference to Question 13, how much is the painting worth after one year?

15.  With reference to Questions 13 and 14, how much is the painting worth after two years?


Practice – Answers
1.  0.09

2.  0.95

3.  4%

4.  45%

5.  45.5%

6.  $12900

7.  $17900

8.  $5500

9.  $22000

10.  $12800

11.  $3200

12.  $7200

13.  $26250

14.  $201250

15.  $231437.50

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