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:
Question:
Convert 7410 to a number in base 5
STEP 1.
Draw a table that looks like “T”
STEP 2.
Put the other base on the TOP LEFT side of your table
| 5 | |
STEP 3.
Put the base 10 number on the TOP RIGHT side of your table
| 5 | 74 |
STEP 4.
Divide the base 10 number by the other base
| 5 | |
STEP 5.
Write your result under the base 10 number
| 5 | |
| 14 |
STEP 6.
Write the remainder in front of your result
| 5 | |
| 14 remainder » 4 |
STEP 7.
Repeat step — 4, 5, 6 for every result until your result is less than the other base
| 5 | |
| 5 | |
| 2 remainder » 4 |
STEP 8.
Once your result is less than the other base, write ZERO as your next result
| 5 | 74 |
| 5 | |
| 5 | |
| 0 |
STEP 9.
Put your last result as the remainder
| 5 | 74 |
| 5 | |
| 5 | |
| 0 remainder » 2 |
STEP 10 — final answer
Write out the remainders from the BOTTOM to the TOP
= 244
FINAL ANSWER:
74 (in base ten)
= 244 (in base five)
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