This document discusses how to convert numbers between different numeric bases: 1) To convert a number from base 10 to another base, use continuous division and write the remainders in the direction of the arrow. 2) To convert a number to base 10 from another base, expand it using the powers of its original base. 3) To convert between two non-base 10 bases, first convert to base 10 as an intermediate step, then convert from base 10 to the target base.

1. Changing from one base to
another
By Albert Mahngo

2. Changing from base 10 to any base
• When changing a number from base 10 to any base, you use
continuous division. Then you write the answer in the direction of
the arrow as illustrated in the picture.
• To convert 27 base 10 to base 5 , you use continuous division as
illustrated above
• You write the answer using remainders in the direction of the arrow.
∴ 𝟐𝟕𝟏𝟎= 𝟏𝟎𝟐𝟓

3. Converting numbers from any base to base 10
• You can also change numbers from any base to base 10
• For you to change a number from any other base to base 10, you
need to expand the number in powers of its base.
• For example if you want to change 348 to base 10. You need to expand
348 in power of its base.

4. Covert 348 to base 10
348 = 3 x 81 + 4 x 80
= 3 x 8+ 4 x 1
= 24 + 4
= 2810
∴ 348= 2810

5. Changing from one base to
another
You can also change from one base to another others than base 10.
For you to convert a number from one base to another base other than
base 10. You need to change the number to base 10 first, followed by a
change to the required base.

6. • For example to change 3405 to base 8
• You need to follow the two steps as follow:
• First step: convert 3405 to base 10
3405 = 3 x 52 + 4 x 51 + 0 x 50
= 3 x 25 + 4 x 5 + 0 x 1
= 75 + 20 + 0
= 9510

7. • Second step: convert 9510 to base 8 using continuous division.
• Write the answer using the remainders in the direction of the arrow:
3405 = 9510 = 1378
∴3405 = 1378