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. (3 points)

Answer 1

rational numbers can be written in form a/b where b≠0

5.2 and 5.5
52/10 and 55/10
so some rational numbers could be
53/10, 54/10


irrational numbers
hmm, most likely the square root numbers
ok, square them
5.2^2=27.04
5.5^2=30.25


5.2<?<5.5
square everybody
27.04<?²<30.25
so pick a number between 27.04 and 30.25
29 or 30 are 2 numbes
I'll pick 29
?²= 29
square root
?=√29
the irrtaional number can be √29
it is 5.39 to the hundreth

Answer 2

Recall what rational numbers are and conversely, what irrational numbers are.
Rational numbers are defined as numbers which can written in fractional notation \frac{a}{b}, where a and b do not have a common factor.

Conversely, irrational numbers cannot be rewritten in fractional form.

As such, an example of a rational number in the interval [5.2, 5.5] is 5.4 because it can be rewritten as \frac{54}{10} = \frac{27}{5}

And an irrational number between the interval can be \sqrt{30}, which comes out to be approximately 5.47723...