   SEARCH HOME Math Central Quandaries & Queries  Question from Angela, a student: I've been searching online for the past week and I cannot find an Algorithm to convert from base 10 to base 5. Can anyone give me a step-by-step instruction on how to do this? Sure Angela,

1. Take the original decimal (base ten) number and call it A.
2. Put a spot on your paper where you will write the equivalent base 5 number from left to right.
3. Divide A by 5 into a quotient Q and a remainder R.
4. Write the remainder R down in the first (ones) column for the base 5 equivalent.
5. Now let A take on the value of Q.
6. Divide A by 5 into a new quotient Q and a new remainder R.
7. Write the remainder R down in the next (working leftwards) column for the base 5 equivalent.
8. Repeat from step 5 until A is zero.

Example: 419 in base 10.

419 ÷ 5 = 83 r 4, so Base 5 is now: _ _ _ 4.

83 ÷ 5 = 16 r 3, so Base 5 is now: _ _ 3 4.

16 ÷ 5 = 3 r 1, so Base 5 is now: _ 1 3 4.

3 ÷ 5 = 0 r 3, so Base 5 is now: 3 1 3 4.

So 419 in base 10 is 3134 in base 5.

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.