Christmas Streak 70/88: Where is wrong? #3

Algebra Level 3

Picture is drawn by me. Picture is drawn by me.

Where is wrong? \text{Where is wrong?}

This problem is a part of <Christmas Streak 2017> series .

Nothing's wrong 1 = 0.99999... 1=0.99999... 1 3 = 0.33333... \dfrac{1}{3}=0.33333... 0.33333... × 3 = 0.99999... 0.33333...\times3=0.99999... 1 3 × 3 = 1 \dfrac{1}{3}\times3=1

Boi (보이) by Boi (보이) , 19, South Korea

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1 solution

Boi (보이)
Dec 9, 2017

Nothing's wrong! 0.99999... 0.99999... does equal 1. 1.

More "formal" proof is as follows:

x = 0.99999... 10 x = 9.99999... 10 x − x = 9.99999... − 0.99999... 9 x = 9 ∴ x = 1 x=0.99999... \\ \\ 10x = 9.99999... \\ \\ 10x - x = 9.99999... - 0.99999... \\ \\ 9x = 9 \\ \\ \therefore x = 1

2 Helpful 0 Interesting 0 Brilliant 0 Confused

How can we prove that 1 3 = 0.333333333333333333333 \dfrac{1}{3}=0.333333333333333333333 ?

Sumukh Bansal - 3 years, 6 months ago

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Work it out as long division; then you'll see.

Blan Morrison - 3 years, 6 months ago

Seriously?

Sathvik Acharya - 3 years, 5 months ago

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