# What numbers added to #0.4# will produce an irrational number?

##### 2 Answers

You didn't provide what numbers to choose, but any irrational number plus a rational number produces another irrational number. For instance...

#pi + 0.4# is irrational. You get something like#3.5415926535cdots#

#sqrt(2) + 0.4# is irrational. You get something like#1.814213cdots#

So the number with infinitely repeating decimals (the one that looks like it will have more digits than your calculator wants to show) is irrational. By definition it means it cannot be represented as a fraction with whole numbers in the top and bottom of the fraction.

So:

#35/50# is not irrational

#1.2434# is not irrational if this is exact

#sqrt3# is irrational because it cannot be represented as a fraction with all whole numbers in the top and bottom.

#pi (3.1415926535cdots)# and#e(2.718281828cdots)# are irrational

etc (see this article to see how#e# is irrational).

Any irrational number when added to 0.4 produce an irrational sum.

Example:

#### Explanation:

There are irrational numbers that are special and crop up all over the place. One of them is used in working out the area of a circle and that number is

Add a rational number such as

So

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A rational number can be expressed as a fraction. That is, it has the form

A well known on is

A denominator of 11 is a good one

An irrational number can

Note that