# Help for Math Project

**Definition.** A rational number is a number that can
be written as a quotient of two integers ,
where b≠ 0.

**Proposition. **Every rational number can be written as an infinite
repeating decimal. E.g.

The bar over 3, indicates that the number 3 repeats indefinitely.

**Definition. **A perfect square is an integer whose square root is another
integer. E.g.

so,

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, . . .

are perfect squares .

**Definition. **An irrational number is a number that can not be written as a
quotient of two integers
,

where b≠ 0.

**Proposition.** In particular, a square root that is not equal to an integer
is an irrational number.

**Proposition. **An irrational number is a number that has a nonterminating,
nonrepeating decimal represen-

tation.

**
Problem.** Is a rational or
irrational number?

9 <10 < 16

calculating the square root to the previous expression ,

Since there is no integer between 3 and 4, is not equal to an integer, so it is an irrational number .

**Procedure.**You may obtain a rational number between other two taking the average of these two numbers:

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