I think the easiest way to think about this is to placed 0.25 into fractional form. 0.25 = 1/4 since 4 separated into 1 = 0.25

So 1/4 included to 2/9 will give us a portion (rational number). Of food to determine what the portion is, we have actually to get a typical denominator.

You are watching: Which number produces a rational number when multiplied by ?

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

The other selections are every irrational numbers and also if you include an irrational number to a reasonable number you acquire an irrational number.

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Consider the meaning of a reasonable number: It needs to be precisely defined by an integer fraction.

For example: 1/3 offers an limitless decimal: 0.33333...., yet the fractional type is precise---multiply by 3 and also you get specifically 1.

Numbers such together π or ε have no specific fractional equivalent.

Many repeating decimals have actually a fountain equivalent. Examples include 1/7 = 0.142857

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

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

Thought problem: room all NON-repeating decimals rational?

We know that 1.375 is rational (it equals 1 and also 3/8, i beg your pardon is 11/8), but how about 1.376?

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