I think the easiest method to think about this is to placed 0.25 into fractional form. 0.25 = 1/4 due to the fact that 4 separated into 1 = 0.25

So 1/4 added to 2/9 will provide us a fraction (rational number). Of food to recognize what the fraction is, we have actually to get a usual denominator.

You are watching: Which number produces a rational number when multiplied by 1/3

(In situation you want to recognize what that rational number is: The least usual denominator would certainly be 36. So changing 1/4 by multiply top and also bottom by 9 provides 9/36 and an altering 2/9 by multiply top and bottom by 4/4 provides 8/36 and adding 9/36 to 8/36 offers 17/36 - a reasonable number.)

The other options are every irrational numbers and also if you include an irrational number come a reasonable number you gain an irrational number.

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Consider the meaning of a rational number: It has to be precisely characterized by an essence fraction.

For example: 1/3 offers an limitless decimal: 0.33333...., but the fractional type is precise---multiply through 3 and you get exactly 1.

Numbers such as π or ε have actually no specific fractional equivalent.

Many repeating decimals have a spring equivalent. Examples encompass 1/7 = 0.142857

(replace the underline v a bar on height of the numbers---that offers you the standard notation because that a repeating group

2/9 + 1/4 = 8/36 + 9/36 = 17/36

Thought problem: space all NON-repeating decimal rational?

We know that 1.375 is reasonable (it amounts to 1 and 3/8, which is 11/8), yet how around 1.376?

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