prata wrote:Which of the following has a decimal equivalent that is a terminating decimal?
I. 1/12
II. 1/(10^2)
III. 1/(2^10)
I only
II only
I and II
I and III
II and III
Let's say that
x = a/b where the fraction a/b is written in
simplest terms.
There's a nice rule that says something like,
If a/b results in a terminating decimal, then the denominator, b, MUST be the product of 2's and 5's only!
So, for example, if b = 20, the fraction a/b will result in a terminating decimal. The same holds true for other values of b such as 4, 5, 25, 40, 2, 8, and so on.
Now onto the question............
I. 1/12
Here the denominator (12) CANNOT be written as a product of 2's and 5's only. So, 1/12 will NOT result in a terminating decimal.
II. 1/(10²)
Here the denominator (10²) CAN be written as a product of 2's and 5's only. So, 1/(10²) WILL result in a terminating decimal.
III. 1/(2^10)
Here the denominator (2^10) CAN be written as a product of 2's s only. So, 1/(2^10) WILL result in a terminating decimal.
Answer:
E
Cheers,
Brent
