Lesson 14
Adding and Subtracting with Scientific Notation
Let’s add and subtract using scientific notation to answer questions about animals and the solar system.
Problem 1
Evaluate each expression, giving the answer in scientific notation:
 \(5.3 \times 10^4 + 4.7 \times 10^4\)
 \(3.7 \times 10^6  3.3 \times 10^6\)
 \(4.8 \times 10^{\text3} + 6.3 \times 10^{\text3}\)
 \(6.6 \times 10^{\text5}  6.1 \times 10^{\text5}\)
Problem 2
 Write a scenario that describes what is happening in the graph.
 What is happening at 5 minutes?
 What does the slope of the line between 6 and 8 minutes mean?
Problem 3
Apples cost $1 each. Oranges cost $2 each. You have $10 and want to buy 8 pieces of fruit. One graph shows combinations of apples and oranges that total to $10. The other graph shows combinations of apples and oranges that total to 8 pieces of fruit.

Name one combination of 8 fruits shown on the graph that whose cost does not total to $10.

Name one combination of fruits shown on the graph whose cost totals to $10 that are not 8 fruits all together.

How many apples and oranges would you need to have 8 fruits that cost $10 at the same time?
Problem 4
Solve each equation and check your solution.
\(\text2(3x4)=4(x+3)+6\)
\(\frac12(z+4)6=\text2z+8\)
\(4w7=6w+31\)
Problem 5
Ecologists measure the body length and wingspan of 127 butterfly specimens caught in a single field.
 Draw a line that you think is a good fit for the data.
 Write an equation for the line.
 What does the slope of the line tell you about the wingspans and lengths of these butterflies?
Problem 6
The two triangles are similar. Find \(x\).