# Questions tagged [number-comparison]

Tag for problems about comparing explicitly given numbers, often by hand calculation only.

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### How do you find by what percent a number is more or less than another number. [closed]

Lets say by what percent 50 is less than 100? (100-50/100)*100 (100-50/50)*100 over here which of the following options are right 1 or ...
1 vote
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### How to show $2\sin 1 < \log_3 (7)$? [closed]

How to show $2\sin 1 < \log_3 (7)$? $1$ is in radians - tried numerically and found it's true. But is there another way to prove it, either geometrically or via algebra? Can't seem to find a ...
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### What is the meaning of $1$ in a relative error?

If we measure a length and is measured as $12.5$ meters long, accurate to $0.1$ of a meter this means the absolute error is $0.05$m. The relative error is: $\frac{0.05}{12.5} = 0.004$. This means that ...
216 views

### Correct comparison of real number for n digits precision (absolute vs relative difference)

To compare if $2$ real numbers are equal, we define a desirable precision e.g. $n$ digits and then check if the following condition holds: $-\frac{1}{10^n} \lt x - y \lt \frac{1}{10^n}$ Now I was ...
393 views

### Comparing $2^{317}$ and $81^{50}$ by hand

How to compare these two numbers without calculator: $2^{317}$ and $81^{50}$ (Pen & paper test) I thought about using logarithms and doing Taylor approximation, but these numbers are close to one ...
1 vote
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### Invariance of number properties under different bases

Are in number theory always numbers with basis 10 considered? I‘m asking which role the basis plays in number theoretic properties or notions like prime numbers for examples. For example: the number 3 ...
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### How to solve this problem on comparison and use the value of average? [closed]

Question: " 6 articles A,B,C,D,E and F are sold at a different price. B is costlier than only 2 items and C is not one of them. D is cheaper than A and is costlier than F, which is costlier than ...
111 views

### Numbers with 1000 digits which are the sum of the 1000th powers of their digits

In the book$^1$ that I am reading, the author dubs an $n$-digit positive number a Smallbrain number if it is equal to the sum of the $n$th powers of its digits, with $371 = 3^3 + 7^3 + 1^3$ given as ...
1 vote
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### Comparing $\sqrt{5} + \sqrt{6} + \sqrt{11}$ and $8$ without calculating the values [closed]

I want to compare $\sqrt{5} + \sqrt{6} + \sqrt{11}$ and $8$ without calculating the actual value of square roots. I tried to apply square on both side but it still carries the root terms. Any trick I ...