Question

Multiply 342 base 5 and 14 base 5 giving answer in base 5

Answer 1

The result of the multiplication is
`11443_5`

In a positional numeral system, the number base, also called the radix, is the total number of distinct digits or symbol combinations that are used to represent numbers. To put it another way, it's the method of counting that's used to express numbers.

We can convert each number to base 10 and convert the results back to base 5.

To convert 342 to base 10

(3 *
`5^2`) + (4 *
`5^1`) + (2 *
`5^0`)

75 + 20 + 2

=97

To convert 14 to base 10

(1 *
`5^1`) + (4 *
`5^0`)

5 + 4

= 9

Then multiply 92 by 9 in 10 we have 97 * 9 = 873

Then we convert back to base 5 and have
`11443_5`