Do you know your bases?

Number Theory Level 2

$\large 2015_7 = ?$

The expression above shows 2015 in base 7. What is this the equivalent of in base 10?

Do you understand different bases? If not head over to the wiki page for help solving this puzzle.

The answer is 698.

1 solution

Stewart Feasby
May 6, 2015

2015 in base 7 can be written in base 10 as: $(2\times 7^3) + (0\times 7^2) + (1\times 7^1) + (5\times 7^0)$ This can be simplified to: $(2\times 343) + (1\times 7) + (5)$ Which simplifies further to: $686 + 7 + 5 = \boxed{698}$ Therefore providing an answer in base 10, as required.

Do you know your bases?

Do you understand different bases? If not head over to the wiki page for help solving this puzzle.

The answer is 698.

1 solution

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