Find the exact value of without using a calculator.
A)3
B)2
C)1.5
D)0.75

Question

Find the exact value of  without using a calculator.
A)3 
B)2 
C)1.5 
D)0.75

Quizplus · Accepted Answer

This is a hexadecimal number, which means each digit represents a multiple of a power of 16. Starting from the right, the first digit represents 11 * 16^28, the second digit represents 14 * 16^24, and so on. However, all of the digits after the underscore (TB8633) do not affect the first digit, so we can ignore them. When we simplify the calculation for the first digit, we get:
11 * 16^28 = 11 * (2^4)^7 = 11 * 2^28 * 2^28 * 2^28 * 2^28 * 2^28 * 2^28 * 2^28
Since 11 and 2^28 are both factors of 2, this simplifies to an even number multiplied by 11. Therefore, the last digit of the exact value is either 2 or 6, depending on whether the even number is divisible by 5. In this case, the even number is the product of seven factors of 2, so it is definitely divisible by 5. Therefore, the last digit is 6, which means the entire number is closer to 1 than to 2. Therefore, the best choice is E) 1.

Find the Exact Value of Without Using a Calculator