The presentation shows how you convert numbers from one base to another

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