1. Jules Henri Poincaré (1854-1912) France
Jules Henri Poincaré ( ) France. Known as a mathematician, theoretical physicist, philosopher of science and engineer. He left an impact on pure and applied mathematics along with mathematical physics, and celestial mechanics.
Poincaré quote: “The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.”

2. Warm Up 1. Write 0.03 as a percent. 2. Write as a decimal.
Find each value. Round to the nearest tenth
if necessary.
3. Find 10% of 53. 3%
0.045
5.3

3. Objectives Use common applications of percents.
Estimate with percents.

4. Caution!
You must convert a percent to a decimal or a fraction before doing any calculations with it.

5. Example 1: Business Application
Mr. Cortez earns a base salary of $26,000 plus a sales commission of 5%. His total sales for one year were $300,000. Find his total pay for the year.
total pay = base salary + commission
Write the formula for total pay.
= base + % of total sales
Write the formula for commission.
= 26, % of 300,000
Substitute values given in the problem.
= 26,000 + (0.05)(300,000)
Write the percent as a decimal.
= 26, ,000
Multiply.
= 41,000
Add.
Mr. Cortez’s total pay was $41,000.

6. Check It Out! Example 1
A telemarketer earns $350 per week plus 12% commission on sales. Find her total pay for a week in which her sales were $940.
total pay = base salary + commission
Write the formula for total pay.
= base + % of total sales
Write the formula for commission.
= % of 940
Substitute values given in the problem.
= (0.12)(940)
Write the percent as a decimal. =
Multiply. =
Add.
The telemarketer’s total pay was $

7. I = P r t Simple Interest Paid Annually
Interest is the amount of money charged for borrowing money, or the amount of money earned when saving or investing money. Principal is the amount borrowed or invested. Simple interest is interest paid only on the principal.
Simple Interest Paid Annually I = P r t
Simple interest
Time in years
Principal
Interest rate per
year as a decimal

8. Example 2A: Financial Application
Find the simple interest paid for 3 years on a $2500 loan at 11.5% per year.
I = Prt
Write the formula for simple interest.
I = (2500)(0.115)(3)
Substitute known values. Write the interest rate as a decimal.
I =
Multiply.
The amount of interest is $

9. Example 2B: Financial Application
After 6 months, the simple interest earned on an investment of $5000 was $45. Find the interest rate.
Write the formula for simple interest.
I = Prt
Substitute the given values.
Multiply Since r is multiplied by 2500, divide both sides by 2500 to undo the multiplication.
45 = 2500r
0.018 = r
The interest rate is 1.8%.

10. Helpful Hint
When you are using the formula I= Prt to find simple interest paid annually, t represents time in years. One month is year.

11. Check It Out! Example 2a
Find the simple interest earned after 2 years on an investment of $3000 at 4.5% interest earned annually.
Write the formula for simple interest.
I = Prt
I = (3000)(0.045)(2)
Substitute the given values.
Multiply.
I = 270
The interest earned is $270.

12. Check It Out! Example 2b
The simple interest paid on a loan after 6 months was $306. The annual interest rate was 8%. Find the principal.
Write the formula for simple interest.
I = Prt
306 = (P)(0.08)
Substitute the given values.
Multiply Since P is multiplied by 0.04 , divide both sides by 0.04.
306 =.04P
7650 = P
The remaining principal is $7650.

13. Practice
1. A computer salesperson earns a base salary of $32,000 per year plus a commission of 6% on total sales. Total sales for one year were $350,000. Find the salesperson’s total pay for the year.
$53,000
2. Find the simple interest paid for 9 months on a a $500 loan at 8% per year.
$30
3. After 2 years the simple interest earned on an investment of 4000 was $216. Find the interest rate.
2.7%

14. Practice
4. A family’s dinner check was $ Estimate a 15% tip.
About $6.00
5.The sales tax rate is 7.1%. Estimate the sales tax on a television set that costs $399.
About $28