Final answer:
To convert the base ten number 42 to base five, we divide by powers of five, resulting in the base five representation of 132.The base ten number 42, when written in base five, is 21.
Step-by-step explanation:
The base ten number 42, when written in base five, is calculated by dividing the number by increasing powers of five and determining the remainder at each step. To convert from base ten to base five, one must understand the concept of place values and how they relate to the chosen base.
In base ten, each place represents a power of ten. Similarly, in base five, each place represents a power of five. To convert 42 from base ten to base five, we divide 42 by the largest power of five smaller than 42, which is 25 (5^2). 42 divided by 25 gives 1 with a remainder of 17. We write down the 1 and then divide the remainder by the next smallest power of five, which is 5 (5^1). 17 divided by 5 gives 3 with a remainder of 2. Write down the 3 next to the 1. The remainder 2 is our last digit since 2 is less than 5 (5^0). Therefore, the number 42 in base five is written as 132.