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705-805 (Hard)|   Algebra|   Arithmetic|                                 
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AditiDeokar
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0.99999999/1.0001 - 0.99999991/1.0003 = 14 Dec 2025, 23:01
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Similar questions please?
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Bunuel
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0.99999999/1.0001 - 0.99999991/1.0003 = 14 Dec 2025, 23:19
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AditiDeokar
Similar questions please?
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Try checking Arithmetic tag.
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ZahraB
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0.99999999/1.0001 - 0.99999991/1.0003 = 15 Dec 2025, 18:18
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Can anyone provide helpful tips on how to become good at exponent type question? I have been struggling with these questions. The moment I see such questions, I know it is going to be hard for me to answer such question. Any tips would be helpful! thanks.
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\(\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=\)


(A) \(10^{(-8)}\)

(B) \(3*10^{(-8)}\)

(C) \(3*10^{(-4)}\)

(D) \(2*10^{(-4)}\)

(E) \(10^{(-4)}\)



OG 2019 #215 PS00574
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0.99999999/1.0001 - 0.99999991/1.0003 = 15 Dec 2025, 19:10
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Hello Zahra


The key is to write these in powers of 10 and spot if you can divide it somehow and make the big number not so big anymore

Step1:
1st fraction can be rewritten as \([\frac{[99999999}{10^8]}/\frac{[10001}{10^4)}]\) ~ \(\frac{[99999999}{10001]} *\frac{[1}{10^4]}\)

Setp2
Key Spot:

99999999 = 10001*(10000-1)

Now the fraction becomes \(\frac{[10001*(9999)}{10001]}\)* 10^-4 = 9999*10^-4

If you repeat the same steps for the 2nd fraction now:

you will eventually get 9997*10^-4

Now the question is \(\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=\) => [9999-9997]*10^-4 = 2*10^-4
Hope this makes sense!

ZahraB
Can anyone provide helpful tips on how to become good at exponent type question? I have been struggling with these questions. The moment I see such questions, I know it is going to be hard for me to answer such question. Any tips would be helpful! thanks.

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0.99999999/1.0001 - 0.99999991/1.0003 = 15 Dec 2025, 22:43
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ZahraB
Can anyone provide helpful tips on how to become good at exponent type question? I have been struggling with these questions. The moment I see such questions, I know it is going to be hard for me to answer such question. Any tips would be helpful! thanks.

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Theory:

Questions

Check below for more:

Hope this helps.­
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