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Problem

2 Mrs. Sanchez asked her students to lassify the following value as rational or irrational: 0.63591 Ryan thinks the value is irrational because the decimal does not have a pattern. Do you agree with Ryan? Why or why not?

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High School Teacher - Tutor for 6 years

It needs to be determined whether it is a rational number or an irrational number, and the basis is given.

$0.63591$

I disagree with Ryan's assertion that 0.63591 is irrational because it does not have a pattern.

**Because 0.63591 is rational.**

The classification of a number as rational or irrational does not solely depend on the visibility of a pattern in its decimal representation, especially when dealing with finite decimals.

**Rational Numbers**:

A number is considered rational if it can be expressed as the ratio of two integers, that is, in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

**Irrational Numbers:**

A number is irrational if it cannot be expressed as a ratio of two integers. Irrational numbers have non-terminating, non-repeating decimal expansions.

**0.63591:**

The number 0.63591 has a finite number of digits after the decimal point and does not continue infinitely, which means it can be expressed as a ratio of two integers.

$0.63591=0.63591 \times \frac{10000}{100000}$,

$= \frac{0.63591 \times 10000}{100000}$,

$= \frac{63591}{100000}$

**Conclusion:** Therefore, 0.63591 is rational.

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