1. Fractions --> Decimals2 11
To change a fraction to a decimal number, =
.18
 Divide. 1 8 1 8
* ‘top dog’ goes in the house… ) 11 2
* ‘decimal, decimal, zero, zero, zero’ 2
 Noticing a pattern? 11
How do you show repeating
decimals? 9 88 2 11 9

2. Decimals --> Fractions
0.84
To change a decimal to a fraction,
1. READ it
“Eighty four hundredths” 84
100 21 25
÷ 4 =
÷ 4
2. WRITE it as a fraction.
3. REDUCE it
2.005
1. READ it
“Two
and five thousandths” 5
1000
÷ 5 1
200 2 = 2
÷ 5
2. WRITE it as a mixed number.
3. REDUCE it

3. Converting Percents to Fractions2 25 8% 8
100
÷ 4 =
To change a percent to a fraction,
Re-write the percent as a
fraction over 100 11 4
275%
275
100
÷ 25 =
2. Simplify. 9_
250
*If there’s a decimal, move it to the end.
3.6%
3.6
100
36_
1000
÷ 4 = =
… but, what you do to the numerator.. •
… you also do to the denominator

4. Converting Fractions to Percents
To change a fraction to a percent, 7 20
• 5 35
35% = =
1. Check the denominator.
• 5
100
* Can it be changed to 100?
yes
2. Rewrite the fraction with a
denominator of 100.
216
300
÷ 3 72
72% = =
÷ 3
100
3. Write it as a percent.
What if the denominator can’t be changed to 100? 3 7 =
3 ÷ 7
0.4285…
a. Divide
42.85 %
Change to a percent
* slide the decimal 2 to the right
42.9%
c. Slap a percent sign on it.
d. Round to the nearest tenth.

5. Converting Between Decimal and Percents
Percent Quiz Notes
DECIMAL
PERCENT
From a to a
0.13
= .13 =
13%
…move the decimal 2 spaces to the right.
90%
0.9
= .9 =
0.0027
= 0.27 =
0.27% 13 00
= 1300 =
1300% •
PERCENT
DECIMAL
From a to a
0.78
=78 =
78% •
…move the decimal 2 spaces to the left.
0.05
= 5 = 5%
1.75
= 175 =
175% =
0.0008% • •

6. Answer: The total cost of the set of golf balls is $21.15
Sales Tax
Tina bought a set of golf balls sells for $20 and the sales tax is 5.75% of the price. What is the total cost of the set?
Write down your steps:
(price)
(tax rate)
as a decimal
To find the tax,
5.75%
MULTIPLY the PRICE
(20)
(.0575)
by the percent as a DECIMAL.
Next, add the sales tax to the regular price.
1.15
(sales tax) +
20.00
(reg price)
Answer: The total cost of the set of golf balls is $21.15
$21.15
(total cost)

7. Answer: The total cost of the set of meal is $79.61
Tip, then Tax
Linda and Bob went to dinner, received lousy service, and decided to tip the server only 12%. If the prepared foods tax is 4.75%, and they ordered $68.19 of food and drinks, what will they pay?
Write down your steps:
To find the tip,
MULTIPLY the PRICE
12%
by the percent as a DECIMAL.
8.17
(tip)
(68.19)
(0.12)
(price)
(tip rate)
as a decimal +
To find the tax,
MULTIPLY the PRICE
4.75%
by the percent as a DECIMAL.
3.24
(tax)
(68.19)
(.0475)
(price)
(tax rate)
as a decimal +
Next, add the tip and sales tax to the regular price.
68.19
(reg price)
Answer: The total cost of the set of meal is $79.61
$79.61
(total cost)

8. Discount, then Tip, then Tax
Brianna uses a “15% off” coupon for TGI Friday’s. She orders $22.57 of food and drinks, decide to tip 20%, and the food tax is 5 %. What will she pay in total?
Write down your steps: (always find discount first)
22.57
(reg price) –
To find the discount,
MULTIPLY the PRICE
by the percent as a DECIMAL.
15%
3.39
(discount)
(22.57)
(0.15)
(price)
(discount rate)
as a decimal
19.18
Subtract the discount from the food cost to get the sale price.
(sale price) +
To find the tip,
MULTIPLY the PRICE
by the percent as a DECIMAL.
3.84
20%
(tip)
(19.18)
(0.20) +
(price)
(tiprate)
as a decimal
1.05
(tax)
To find the tax,
MULTIPLY the PRICE
by the percent as a DECIMAL.
5.5%
$24.07
(19.18)
(0.055)
(total cost)
(price)
(tax rate)
as a decimal

9. Discount, then Tip, then Tax
Mort and Teddy receive a “15% off” coupon for Bob’s Burgers. They order $22.57 of food and drinks, decide to tip 20%, and the food tax is 5 %. What will they pay in total?
To find the discount, ...
(price) (discount rate)
as a decimal
Multiply the price and the discount rate (as a decimal)
(22.57)(.15)
15%
.15
3.39
Now, subtract the discount from the old price to get the new price.
= 19.18
(19.18)(.20)
= 3.84
To find the tip, multiply the new price and the tip rate (as a decimal)
(19.18)(.055)
= 1.05
To find the tax, multiply the new price and the tax rate (as a decimal)
They paid $24.07
Finally, add them up.

10. Modeling Fractions, Decimals & Percents.

11. I = P•R•T $ I = 180 I = P • R • T I = 1500 • .04 • 3 Finding Interest
Percent Quiz Notes
Gene found a bank offering a certificate of deposit that pays 4% simple interest. He has $1,500 to invest. How much interest will he earn in 3 years?
To find interest, use a formula
I = P•R•T
INTEREST
extra money someone pays when they borrow money.
PRINCIPAL
amount of money you borrow or lend.
RATE
interest rate written as a decimal
TIME
years of the loan
I = P • R • T
Replace the variables:
~ P with $1,500
~ R with .04
~ T with 3.
Why .04? All % must be written as decimals.
I = 1500 • .04 • 3
Answer: Gene will earn $180 in interest in 3 years. $
I = 180
Multiply.

12. Finding Principal, Rate, or Time Joan loaned $12,000 in principal.
Joan works for West Bank, and she just made a car loan at 8.9% interest rate for 5 years. The bank will earn $5,340 in interest. How much principal did she loan?
I = P • R • T
1. Replace the variables:
~ I with ~ P with p
~ R with ~ T with 5.
5340= p • • 5
2. Multiply (rate • time)
5340= p •
3. Divide to find p.
Joan loaned $12,000 in principal.
12,000 = p
Collette put $400 in principal in a savings account for 2 years, and she earned $7.20 in interest. What interest rate was she earning?
Ralph just finished paying off a $3500 loan. He paid an additional $ in interest on his 19.9% loan. What was the length of time on this loan?
I = P • R • T
I = P • R • T
= • R • 2
= • • T
= • R
The rate is 0.009, or 0.9%
= • T
0.009 = R
It was a 30 month loan.
2.5 = T

19. Estimating Percent Mentally
10% Lola borrowed $125 from a pawn shop. She’ll have to pay
back the loan, plus the pawn shop charges an additional
9.9% fee. ≈ how much will her additional fee be?
10%
Step 1: Look at your cost and your percent. Do they need rounding?
~ $125 is OK, but let’s round 9.9% to 10%
Fee is about $12 or $13.
Step 2: To find 10%, slide the decimal 1 space to the left. 5%
15%
20%
25%
50%
do the 10% trick
cut that number in half
do the 10% trick
cut that number in half
add both numbers
do the 10% trick
double that number
do 20%
+ 5% or
mentally divide the number by 4
round your number
cut it in half

20. Estimating Percent Mentally
about $ $0.06 (5 or 6 cents)
≈ $ $30 = $90
(10%) + (5%) = (15%)
≈$ $0.41 (about 40 or 41 cents)
≈ $ $ = $60,000
(10%) (5%) = (15%)
≈ $ $7.40
≈ $4
(10%) •
● (2)
= $8
= (20%)
≈ $59 - $60
≈ $50 00
(10%)
● (2)
= $10,000
(20%)
≈ $ $1200
≈ $ ● 2 = $400,000 - $500,000
(10%) ● 2 = (20%)
$ or $900,000
≈$0.08 (8 cents) 4
= $.02 (2 cents)
(25%)
≈ $1,6 00,000, $2,000,000,000
(1.6 trillion to 2 trillion)
≈ $16 4
≈ $4 - $5
(25%)
≈$.08 (or 8 cents)
-->$0.08 =
(10%)
$.04 (or 4 cents)
(5%)
≈$28,000 4
≈ $7,000
(25%)
≈ $1 - $1.20
(10%)
--> $1 2
= $.50 - $.60
(5%)
≈$400 2
≈ $190 - $200
(50%)
≈ $800
(10%)
--> $800 2
= $400
(5%)
≈$100,000 2
≈ $50,000 - $55,000
(50%)
≈ $.1 2
(10%)
+ $.06
+ (5%)
= $.15 - $.20
= (15%)
≈ $1,000,000 2
≈ $500,000 - $550,000
(50%)

21. Answer: Linda and Bob will pay $79.61.
Tip, then Tax
Linda and Bob went to dinner, received lousy service, and decided to tip the server only 12%. If the prepared foods tax is 4.75%, and they ordered $68.19 of food and drinks, what will they pay?
To find the tip, ...
(price) (tip rate)
as a decimal
Multiply the price and the
tip rate (as a decimal).
12%
(68.19)
(.12)
.12
8.18
Next, to find the tax
Answer: Linda and Bob will pay $79.61.
(price) (tax rate)
Multiply the price
and the tax rate.
(68.19)
(.0475)
4.75%
.0475
3.24
Finally, add them up.