Base 5, 7 or 9?

Number Theory Level 1

20 0 5 10 0 7 5 6 9 \Large \color{#20A900}{200_5} \quad \color{#3D99F6}{100_7} \quad \color{#69047E}{56_9} Which of these numbers is the largest? \text{Which of these numbers is the largest?}

Note : 20 0 5 200_5 means that the number is in base 5 5 , and so forth.

20 0 5 200_5 10 0 7 100_7 5 6 9 56_9 All are equal

Zeeshan Ali by Zeeshan Ali , 25, Pakistan

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1 solution

Kay Xspre
Jan 24, 2016

I put a reservation here first that you should have written the proper number in the choice as well, otherwise it may be very confusing. As for the answer, when rewritten in base 10, this will be 20 0 5 = ( 0 × 1 ) + ( 0 × 5 ) + ( 2 × 5 2 ) = 50 10 0 7 = ( 0 × 1 ) + ( 0 × 7 ) + ( 1 × 7 2 ) = 49 5 6 9 = ( 6 × 1 ) + ( 5 × 9 ) = 51 \begin{matrix} 200_5 = (0\times1)+(0\times5)+(2\times5^2) = 50\\ 100_7 = (0\times1)+(0\times7)+(1\times7^2) = 49\\ 56_9 = (6\times1)+(5\times9) = 51 \end{matrix} Therefore 10 0 7 < 20 0 5 < 5 6 9 100_7 < 200_5 < 56_9

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Brilliant.

Ramesh Kale - 5 years, 4 months ago

For some reason, I interpreted 100base7 as 7^3 oops

Nathan Richardson - 2 years, 5 months ago

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