I Can Do This Division Without A Calculator

What is the value of 41 29 \frac{41}{29} to 5 decimal places?

Hint: Read the Mental Math Tricks wiki.


The answer is 1.41379.

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1 solution

Michael Fuller
Jan 18, 2016

41 29 = 1 + 12 29 \dfrac{41}{29}= 1 + \dfrac{12}{29} . Apply the Division by 29 trick from the Mental Math Tricks wiki on 12 29 \dfrac{12}{29} for 6 lines :

12 3 = 4 remainder 0 4 3 = 1 remainder 1 11 3 = 3 remainder 2 23 3 = 7 remainder 2 27 3 = 9 remainder 0 9 3 = 3 remainder 0 \dfrac{12}{3} = \text{4 remainder 0} \\ \dfrac{4}{3} = \text{1 remainder 1} \\ \dfrac{11}{3} = \text{3 remainder 2} \\ \dfrac{23}{3} = \text{7 remainder 2} \\ \dfrac{27}{3} = \text{9 remainder 0} \\ \dfrac{9}{3} = \, \text{3 remainder 0}

Therefore 41 29 = 1 + 0.413793 = 1.413793 = 1.41379 (5 d.p.) \dfrac{41}{29} = 1 + 0.413793 = 1.413793 = \large \color{#20A900}{\boxed{1.41379 \, \text{(5 d.p.)}}}

Great solution! By the way, Brilliant actually rounds off the answer. So even if you enter 1.414, the answer is correct. I think you should write something like find 1 0 5 41 29 10^5 \cdot \frac{41}{29} .

Arulx Z - 5 years, 4 months ago

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Thanks for mentioning that, I didn't realise it rounded your answers! In that case I will remake this question soon.

Michael Fuller - 5 years, 4 months ago

What's so beneficial about this? Calculator are easily accessible and this really doesn't give any insight! I feel like dumb doing this...

Akshay Krishna - 2 years, 7 months ago

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Yes calculators are easily accessible, but using your own mind to solve a problem is intution and thats all what brilliant is about!

pratibha srivastava - 5 months, 3 weeks ago

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