How to convert a number to base 10?

There are three steps required in converting a number of any base to a base 10 number. These are

Determine the place values (of the given base) of each digit in the number
Each number base system has its own place values. For example, the base 5 system has the place values ones, fives, twenty fives, one hundred twenty fives, six hundred twenty fives, and so on.
The first place value in any number system is 1. Each place value is obtained by multiplying
the previous place value with the base of the number. For example, in the base five number
system, each place value is obtained by multiplying 5 with the previous place value. So, the place
values are 1, 5, 25, 125, 625, and so on.

For example, if a number is 423 of base 5, then the place values of each digit are as follows:

Multiply each digit with its place value (of the given base) to obtain its value
Multiplying each digit with its place value gives its actual value:
  • 4 x 25 = 100
  • 2 x 5 = 10
  • 3 x 1 = 3
Add all the digits value - this will give you the value of the number in base 10
Decimal number (base 10) = 100 + 10 + 3 = 113
Therefore the number 423 of base 5 is equal to the number 113 of base 10.

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