Which number produces a rational number when added to 0.25

Question

A. 2/9

B. 0.2645751311...

C. √2

D. 𝛑

Answer 1

I think the easiest way to think about this is to put 0.25 into fractional form. 0.25 = 1/4 because 4 divided into 1 = 0.25

So 1/4 added to 2/9 will give us a fraction (rational number). Of course to determine what the fraction is, we have to get a common denominator.

(In case you wanted to know what that rational number is: The least common denominator would be 36. So changing 1/4 by multiplying top and bottom by 9 gives 9/36 and changing 2/9 by multiplying top and bottom by 4/4 gives 8/36 and adding 9/36 to 8/36 gives 17/36 - a rational number.)

The other choices are all irrational numbers and if you add an irrational number to a rational number you get an irrational number.

Answer 2

Consider the definition of a rational number: It has to be precisely defined by an integer fraction.

For example: 1/3 gives an endless decimal: 0.33333...., but the fractional form is precise---multiply by 3 and you get exactly 1.

Numbers such as π or ε have no exact fractional equivalent.

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

(replace the underline with a bar on top of the numbers---that gives you the standard notation for a repeating group

I think the only possible answer is A.----add 2/9 to 0.25

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

Thought problem: Are all NON-repeating decimals rational?

We know that 1.375 is rational (it equals 1 and 3/8, which is 11/8), but how about 1.376?