Question

convert

Answer 1

The number 125.3? And you're meant to write it as the quotient of two integers?

Answer 2

i think @SmoothMath , u r not familiar with this question

Answer 3

I'm asking for clarification.

Answer 4

I think its supposed to convert to an irrational number, p/q, since it has a little line over the 3.

Answer 5

yes @some_someone

Answer 6

There's no such thing as "converting to an irrational number." A number is either rational or irrational.

Answer 7

ok this number is irrational, @SmoothMath , but its in decimal, so he wants to convert it to p/q

Answer 8

This number is rational though, so we can express it as the quotient of two numbers p and q, where p and q are integers.

Answer 9

It's rational, @some_someone

Answer 10

If it was irrational, then by definition, you could not write it as p/q, at least assuming p and q were integers.

Answer 11

http://www.mathsisfun.com/definitions/irrational-number.html

Answer 12

okaii then, @SmoothMath , then explain to him how to express it as the quotient of two numbers p and q, where p and q are integers.

Answer 13

Exactly, so this is a repeating decimal, which means it can be written as a fraction. Do you know what the fraction 0.3333... is?

Answer 14

\[\Large 0.\bar3 = \frac{1}{3}\]

Answer 15

@SmoothMath , you are correct, repeating decimals are rational

Answer 16

Interesting approach. You still need for P and Q to be integers though.

Answer 17

In your answer, P = 11279.7 is not an integer.

Answer 18

so, in question there is also written p and q are integers and q is not equal to 0

Answer 19

Exactly.
I think this approach might be simpler for you to work with:
\[\Large0.\bar3 = \frac{1}{3}\]
therefore,
\[\Large125.\bar3 = 125 + \frac{1}{3}\]

Answer 20

Does that much make sense to you?

Answer 21

@SmoothMath and @some_someone