Convert to base 10 - Mathematics Learning Modules

Department of Mathematics

Base 10 System
Convert to Base 10

Conversion to base 10: by expansion method

4123₅=4(5³)+1(5²)+2(5¹)+3(5⁰)= 538₁₀ =538

Base 5
place value 5³ 5² 5¹ 5⁰

Base 5 - expanded 125 25 5 1

Base 10 Equiv.
4123₅ 4x125
=500 1x25
=25 2x5
=10 3x1
=3 sum of row
= 538

4123₈=4(8³)+1(8²)+2(8¹)+3(8⁰)= 2131₁₀ =2131

Base 8
place value 8³ 8² 8¹ 8⁰

Base 8 - expanded 512 64 8 1

Base 10 Equiv.
4123₈ 4x512
=2048 1x64
=64 2x8
=16 3x1
=3 sum of row
= 2131₁₀

*Base 5* *place value*	5³	5²	5¹	5⁰
*Base 5 - expanded*	*125*	25	5	1
*Base 10 Equiv.* 4123₅	*4x125* *=500*	*1x25* *=25*	*2x5* *=10*	*3x1* =3	*sum of row* *= 538*

*Base 8* *place value*	8³	8²	8¹	8⁰
*Base 8 - expanded*	*512*	64	8	1
*Base 10 Equiv.* 4123₈	*4x512* *=2048*	*1x64* *=64*	*2x8* *=16*	*3x1* =3	*sum of row* *= 2131₁₀*