Question

Find a rational number that is between 5.2 and 5.5. Explain why it is rational.Find an irrational number that is between 5.2 and 5.5. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth.

Answer 1

Hello! 

I will provide a quick review below.

Rational Numbers
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Whole Numbers (1, 25, 50)
Integers (-5, 6)
Terminating Decimals (0.5, 0.5266)
Repeating Decimals (1.333333333(1/3) 1/9 (1.1111111111111))

Irrational Numbers
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Repeating Decimals in No Specified Order ($\pi$, √2)
Anything That Cannot Be Written as a Fraction
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Now we can solve the problem. A rational number between 5.2 and 5.5 is 5.3 since it is a terminating decimal and can be written as a fraction ($\frac{53}{10}$).

An irrational number is √26, which is about 5.1 when it is rounded to the nearest hundredth. It is irrational because it is a repeating decimal in no specific order. √26 is actually 5.099019513592... which has no specified order of numbers so therefore it cannot be written as a fraction and is an irrational number.

I hope this helps!