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.
