convert 1.1 base five to a binary number

Answer 1

To convert a number from base five to binary, we need to convert it to base ten first and then convert it to binary.

To convert 1.1 from base five to base ten, we can use the formula:

(1 * 5^0) + (1 * 5^-1) = 1.2 base ten

Now, let's convert 1.2 base ten to binary.

To convert a decimal number to binary, we can multiply the decimal part by 2 repeatedly and keep track of the carryover until the decimal part becomes 0 or until we get the desired level of precision.

1.2 * 2 = 2.4 (take integer part: 1, carryover: 0)
0.4 * 2 = 0.8 (take integer part: 0, carryover: 0)
0.8 * 2 = 1.6 (take integer part: 1, carryover: 0)
0.6 * 2 = 1.2 (take integer part: 1, carryover: 0)
0.2 * 2 = 0.4 (take integer part: 0, carryover: 0)
0.4 * 2 = 0.8 (take integer part: 0, carryover: 0)
0.8 * 2 = 1.6 (take integer part: 1, carryover: 0)
0.6 * 2 = 1.2 (take integer part: 1, carryover: 0)

The decimal part repetitively yields 1, 0, 1, 1, 0, 0, 1, 1...

Therefore, 1.1 base five is approximately equal to 1.10110011... base two.