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Illustrative Math
Grade 8
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)
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 × 10^{8} km from the Sun, while Mercury is about 5.8 × 10^{7} km. In order to find
1.5 × 10^{8} - 5.8 × 10^{7}
we can rewrite this as
1.5 × 10^{8} - 0.58 × 10^{8}
Now that both numbers are written in terms of 10^{8}, we can subtract 0.58 from 1.5 to find
0.92 × 10^{8}
Rewriting this in scientific notation, the Earth is
9.2 × 10^{7}
km further from the Sun than Mercury.
Mentally decide how many non-zero digits each number will have.
Diego, Kiran, and Clare were wondering:
“If Neptune and Saturn were side by side, would they be wider than Jupiter?”
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?
37, 32, 16, 8, 4, 2, 1
Use the table to answer questions about different life forms on the planet.
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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