Answer:
1) Yes, it is rational.
2) Yes, it is rational.
3) There are three repeating digits.
Step-by-step explanation:
Lets solve them in order.
1) First lets see what the characteristics of a rational number are. We know that, to be a rational number, a number must either:
- Can be expressed as a fraction
- Repeat
- Are integers
- And terminate
An irrational number is a number that never repeats or ends. They are also not integers, but we will focus on the never repeats or ends part.
So, lets look at it. Does 0.147 repeat, terminate, be expressed as a fraction, and is it an integer? Well, its not an integer, it doesn't repeat, and it isn't a fraction. However, it does terminate, which means it is rational.
2) Is 0.147 repeating a rational or irrational number. Remember, we need to see if it terminates, repeats, is an integer, or is a fraction. Well, it doesn't terminate, it is not a fraction, and it is not an integer. However, it does repeat. That means that it is a rational number.
3) Now, to figure out how many repeating digits there are. In math, we know that the line above the numbers in the decimal place means that they repeat. So simply find out how many digits are below that line. Well, we see that 1, 4, and 7 are under the line. In total that is three digits. So the answer is 3.
