Answer:
To convert 1/4 to base 2, we need to use the method of repeated multiplication by 2. This means that we multiply the fraction by 2, and write down the integer part of the result as the first digit of the binary representation. Then, we take the fractional part of the result and multiply it by 2 again, and write down the integer part as the second digit. We repeat this process until we either get a fractional part of zero, or reach the desired number of digits. For example:
1/4 * 2 = 1/2 + 0 0.5 * 2 = 1 + 0 0 * 2 = 0 + 0
The binary representation is obtained by reading the digits from right to left, so we get:
1/4 = 0.01 in base 2
Alternatively, we can use a shortcut by observing that 1/4 is equivalent to 2^-2, which means that it has a binary representation of 0. followed by two zeros and a one. Therefore, we can also write:
1/4 = 0.001 in base 2