Converting from base 10 to other bases, including to base 2, requires the use of a method called “repeated division.”
In this lesson, you will learn the step-by-step method of using repeated division to convert base 10 to other bases.
BONUS: A link to practice questions on number bases is included at the end of this lesson.
Question on converting base 10 to other bases
Let’s take an example:
Convert 7410 to a number in base 5
Draw a table that looks like “T”
Put the other base on the TOP LEFT side of your table
Put the base 10 number on the TOP RIGHT side of your table
Divide the base 10 number by the other base
Write your result under the base 10 number
Write the remainder in front of your result
|14 remainder » 4|
Repeat step — 4, 5, 6 for every result until your result is less than the other base
|2 remainder » 4|
Once your result is less than the other base, write ZERO as your next result
Put your last result as the remainder
|0 remainder » 2|
STEP 10 — final answer
Write out the remainders from the BOTTOM to the TOP
74 (in base ten)
= 244 (in base five)
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