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PART B Write the two weights using a different power of 10 that would still allow the numbers to be subtracted. Show your work.

I just don't understand what it's asking​

PART B Write the two weights using a different power of 10 that would still allow-example-1
User Koceeng
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1 Answer

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You're probably familiar with the idea that something like 3m-4n cannot be simplified since we don't have like terms here.

The same idea applies for this scientific notation. It's not entirely obvious, but what we can do is let m = 10^(-4)

This would mean 8.8 x 10^(-4) turns into 8.8 x m or 8.8m for short

Then let n = 10^(-3)

The 2.2 x 10^(-3) becomes 2.2 x n or 2.2n for short.

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The original numbers have become 8.8m and 2.2n

Subtracting them means 8.8m - 2.2n

We cannot simplify that because m and n are different

Your teacher wants you to rewrite one of the scientific notation numbers so that we have the same 10^(something) term.

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I'll rewrite 2.2 x 10^(-3) in terms of something times 10^(-4)

Notice that 10^(-3) = 10^(-4+1) = 10^(-4)*10 = 10*10^(-4)

So,

2.2 x 10^(-3) = 2.2 x 10*10^(-4)

2.2 x 10^(-3) = 22 x 10^(-4)

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At this point we have

  • egg A with weight 8.8 x 10^(-4) lbs
  • egg B with weight 22 x 10^(-4) lbs

Both involve 10^(-4) now. We have like terms

Recall that we made m = 10^(-4)

  • Egg A = 8.8 x 10^(-4) = 8.8m
  • Egg B = 22 x 10^(-4) = 22m

Subtract the values:

22m - 8.8m = 13.2m

13.2m = 13.2 x 10^(-4)

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The last step is to convert back to scientific notation

13.2 x 10^(-4)

(1.32 x 10^1) x 10^(-4)

1.32 x (10^1*10^(-4))

1.32 x 10^(1-4)

1.32 x 10^(-3)

This represents the difference in the two weights, i.e. how much heavier egg B is compared to egg A.

The units for this answer is "pounds" or "lbs" for short.

User CJCombrink
by
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