Lesson 15: Adding and Subtracting with Scientific Notation
Let’s add and subtract using scientific notation to answer questions about animals and the solar system.
Illustrative Math Unit 8.7, Lesson 15 (printable worksheets)
Lesson 15 Summary
When we add decimal numbers, we need to pay close attention to place value. For example, when we calculate 13.25 + 6.7, we need to make sure to add hundredths to hundredths (5 and 0), tenths to tenths (2 and 7), ones to ones (3 and 6), and tens to tens (1 and 0). The result is 19.95.
We need to take the same care when we add or subtract numbers in scientific notation. For example, suppose we want to find how much further the Earth is from the Sun than Mercury. The Earth is about 1.5 × 108 km from the Sun, while Mercury is about 5.8 × 107 km. In order to find
1.5 × 108 - 5.8 × 107
we can rewrite this as
1.5 × 108 - 0.58 × 108
Now that both numbers are written in terms of 108, we can subtract 0.58 from 1.5 to find
0.92 × 108
Rewriting this in scientific notation, the Earth is
9.2 × 107
km further from the Sun than Mercury.
Lesson 15.1 Number Talk: Non-zero Digits
Mentally decide how many non-zero digits each number will have.
Lesson 15.2 Measuring the Planets
Diego, Kiran, and Clare were wondering:
“If Neptune and Saturn were side by side, would they be wider than Jupiter?”
- They try to add the diameters, 4.7 × 104 km and 1.2 × 105 km. Here are the ways they approached the problem. Do you agree with any of them? Explain your reasoning.
a. Diego says, “When we add the distances, we will get 4.7 + 1.2 = 5.9. The exponent will be 9. So the two planets are 5.9 × 109 km side by side.”
b. Kiran wrote 4.7 × 104 as 47,000 and 1.2 × 105 as 120,000 and added them:
120,000 + 47,000 = 167,000
c. Clare says, “I think you can’t add unless they are the same power of 10.” She adds 4.7 × 104 km and 12 × 104 to get 16.7 × 104.
- Jupiter has a diameter of 1.43 × 105. Which is wider, Neptune and Saturn put side by side, or Jupiter?
Lesson 15.3 A Celestial Dance
- When you add the distances of Mercury, Venus, Earth, and Mars from the Sun, would you reach as far as Jupiter?
- Add all the diameters of all the planets except the Sun. Which is wider, all of these objects side by side, or the Sun? Draw a picture that is close to scale.
Are you ready for more?
The emcee at a carnival is ready to give away a cash prize! The winning contestant could win anywhere from $1 to $100. The emcee only has 7 envelopes and she wants to make sure she distributes the 100 $1 bills among the 7 envelopes so that no matter what the contestant wins, she can pay the winner with the envelopes without redistributing the bills. For example, it’s possible to divide 6 $1 bills among 3 envelopes to get any amount from $1 to $6 by putting $1 in the first envelope, $2 in the second envelope, and $3 in the third envelope (Go ahead and check. Can you make $4? $5? $6?).
How should the emcee divide up the 100 $1 bills among the 7 envelopes so that she can give away any amount of money, from $1 to $100, just by handing out the right envelopes?
Lesson 15.4 Old McDonald’s Massive Farm
Use the table to answer questions about different life forms on the planet.
- On a farm there was a cow. And on the farm there were 2 sheep. There were also 3 chickens. What is the total mass of the 1 cow, the 2 sheep, the 3 chickens, and the 1 farmer on the farm?
- Make a conjecture about how many ants might be on the farm. If you added all these ants into the previous question, how would that affect your answer for the total mass of all the animals?
- What is the total mass of a human, a blue whale, and 6 ants all together?
- Which is greater, the number of bacteria, or the number of all the other animals in the table put together?
Lesson 15 Practice Problems
- Evaluate each expression, giving the answer in scientific notation:
- a. Write a scenario that describes what is happening in the graph.
b. What is happening at 5 minutes?
c. What does the slope of the line between 6 and 8 minutes mean?
- 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.
a. Name one combination of 8 fruits shown on the graph that whose cost does not total to $10.
b. Name one combination of fruits shown on the graph whose cost totals to $10 that are not 8 fruits all together.
c. How many apples and oranges would you need to have 8 fruits that cost $10 at the same time?
- Solve each equation and check your solution.
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