Explain whether each decimal number represents a rational number.

(a) 0.16

(b) 0.12

(c) -3.125

(d) -0.27

(e) -0,212 112 111 2 ....

(f) 0. 457 92

If it wouldn't be a problem i would really appreciate it if you sent back the instructions on how to do the question.

My name is Kristin

Thank-you for you time

Hi Kristin

A rational number is one that can be written as a positive or negative fraction (a/b) where a and b are integers, so you need to decide whether or not you can re-write each of these decimal fractions in the form a/b. Decimals that can be written as a/b have either a finite number of places after the decimal as 3/4 = 0.75, or a decimal part that repeats as 3/7 = 0.428 571 428 571...

(a) can be written as 16/100 and so it is rational.

(c) can be written as -3125/1000 and it is also rational.

(e) cannot be written as a fraction since it goes on forever and does not repeat (If it repeated you would be able to change it to a fraction.) so it is not a rational number and is called an irrational number.

This is probably the answer that is expected for part (e) but it is not absolutely clear that this is the correct answer. Perhaps the number is actually -0,212 112 111 212 112 111...

You should now be able to do the rest of the questions.

Good luck!
Jack