Quick review of concepts
Percents: A percent is a ratio whose second term is 100 (so, 90:100 is 90%); another way to look at percents is in terms of fractions (such as ¾ is the same as 3 divided by 4, which is 0.75 or 75%). Essentially, percent means “parts” per hundred.

EX.
20% = 20/100 = 1/5

4/3 = 0.75 = 75/100 = 25%

1.34 = 134/100 = 134%

Scientific Notation:
Put the decimal after the first digit; to find the exponent (the power of 10), count the number of places from the decimal to the end of the number.

EX.
126,000,000 = 1.26 × 10⁸

6,000,000 = 6.0 × 10⁶

2,126,000,000 = 2.13 × 10⁹

**Not sure if this will be tested, but if you want to add numbers that use scientific notation, you have to make sure that the exponents are the same before you add (so 1.2 × 10² + 1.2 × 10² = 2.4 × 10², but 1.2 × 10² + 1.2 × 10³ = 1.2 × 10² + 12 × 10² = 13.2 × 10²). Let me know if you have seen problems like that and we can review them.

Practice Problems
Percent Problems
1. If a discount of 50% off the retail price of a dress saves Laquasha $100, how much did she pay for the dress?

2. Tony pays $1,000 in state taxes on a newly purchased car. What is the value of the car if state taxes are 10% of the value?

3. How many years does Steven need to invest his $3,000 at 7% to earn $210 in simple interest?

4. Sabrina’s boss states that she will increase Sabrina’s salary from $12,000 to $14,000 per year if she enrolls in business courses at a local community college. What percent increase in salary will result from Sabrina taking the business courses?

5. 35% of what number is 70?

6. What number is 5% of 2000?

7. What percent of 90 is 27?

8. If 45 is 120% of a number, what is 50% of the same number? (hint: set up the bow tie just as you would with a regular 100% question)

9. What is 30% of a number if 30 is 15% of a number? (hint: set up the bow tie just as you would with a regular 100% question)

11. Which of these percentages equals 1.25? (hint: remember that in number form 1.00 = 100%; a percent is a fraction with 100 in the denominator)

a. 25%
b. 125%
c. 1½%

12. Which of the following percentages is equal to 0.45? (hint: remember that in number form 1.00 = 100%; a percent is a fraction with 100 in the denominator)

a. 45%
b. 450%
c. 4½%

13. 22% of $900 =

14. 25% of 400 =

15. If 10 is 20% of a number, what is 40% of the same number

Scientific Notation Problems
1. Convert the following numbers to scientific notation:

a. 3,897,000 =
b. 23 =
c. 45,000 =
d. 900 =

2. Convert the following scientific notation to regular numbers:

6.2356 × 10⁹ =
1.34 × 10^{2 2.02 × 1011 =
9.442 × 106 =
3.12 × 103 =
1.5 × 107 =}

Please post to comments if you have any questions (no registration required). I will update Square Root and Word Problems tomorrow.

Hope this helps!