Define: Percent Increase or Decrease
Define: Name some large number situations that you would want to use SN to solve instead of standard form.
Define: Name some small number situations that you would want to use SN to solve instead of standard form.
#1: In 2013 the Los Angeles Dodgers opening day payroll was about $2.16 × 10^8 and the Houston Astros opening day payroll was about $2.4 × 10^7. How much higher was the Dodgers’ payroll?
#2: A TV show had 3.5 × 10^6 viewers for their first episode and 8.5 × 10^6 viewers for their second episode. How many viewers did they have overall?
#3: A dime is approximately 1.35 x 10^−1cm thick. The thickness of a dollar bill is approximately 1.2 x10^−2. How many times greater is the thickness of a dime than the thickness of a dollar bill?
#4: A corporation earned a profit of $2.5 × 10^4 for 1 × 10^3 days in a row. What was the corporation’s total profit during this time period?
#5: Write a division problem in which two numbers written in scientific notation have a Sum of 5 x 10^-5.
Percent Increase or Decrease: The percent difference between a new and original value, calculated by dividing the difference by the original value and multiplying by 100.
Large number situations where you would use scientific notation:
- Payrolls of sports teams
- Population of a country
- GDP of a nation
Small number situations where you would use scientific notation:
- Thickness of materials (like in #3)
- Distance between objects at micro or nano scales
- Accuracy of scientific measurements
#1: To find how much higher the Dodgers' payroll was, subtract the Astros' payroll from the Dodgers' payroll:
($2.16 × 10^8) - ($2.40 × 10^7) = $2.16 × 10^8 - $2.40 × 10^7 = $1.92 × 10^8
#2: To find the overall viewership of the TV show, add up the viewers for the first and second episodes:
(3.5 × 10^6) + (8.5 × 10^6) = 3.5 × 10^6 + 8.5 × 10^6 = 12 × 10^6 = 1.2 × 10^7 viewers
#3: To find how many times greater the thickness of a dime is than a dollar bill, divide the thickness of the dime by the thickness of the dollar bill:
(1.35 × 10^-1) / (1.2 × 10^-2) = 1.35 × 10^-1 / 1.2 × 10^-2 = 1.125 = 11.25 times greater
#4: To find the corporation's total profit, multiply the profit per day by the number of days:
($2.5 × 10^4) * (1 × 10^3) = $2.5 × 10^4 * 1 × 10^3 = $2.5 × 10^7 total profit
#5: A division problem with a sum of 5 x 10^-5 in scientific notation might look like:
(3 x 10^-5) ÷ (2 x 10^-5) = 1.5 x 10^0 = 1.5