Question

Help! with Irrational and Rational #!!!

Answer 1

Hai Here to help

Answer 2

First off do you know what irrational and rational numbers are?

Answer 3

So pi is irrational.

Answer 4

So that shows that the first one is....

Answer 5

An irrational number is any real number that cannot be expressed as a ratio of integers.A rational number is a number that can be written as a ratio.

Answer 6

Divide pi by 2 and tell me what you get

Answer 7

Rational!

Answer 8

Try again...

Answer 9

Irrational!

Answer 10

If you do 3.14/2 you get something like 1.57 But all the other digits are behind it...they just don't show it

Answer 11

ok what about...\[\sqrt{90}\]

Answer 12

Now 2nd one

Type 90 into your calculator and click the sqrt root button...What do you get?

Answer 13

Well...rounded i got...9.49

Answer 14

un~rounded~~9.486

Answer 15

So 90 is irrational or rational?

Answer 16

\[\sqrt{90}\]

Answer 17

Well the number goes on and on right?

Answer 18

A rational number is a number that can be written as the ratio of two whole numbers. (note how "ratio" is in the word "rational")

So any number \(\dfrac{a}{b} \text{ where } b\neq 0\) is a rational number.

Whole numbers are rational too! \(10 = \dfrac{10}{1}\) for example.

Repeating decimals are rational too! \(0.428571428571428571\ldots = \dfrac{3}{7}\)

Prefect squares are rational: \(\sqrt{81}=9=\dfrac{9}{1}\)

Ratios of perfect squares are rational: \(\dfrac{\sqrt{9}}{\sqrt{49}}=\frac{3}{7}\)

The following are NOT rational:

Numbers like \(\pi, e\) or any multiple of those numbers. The square root of imperfect squares: \(\sqrt{5}\) or \(\sqrt{75}=\sqrt{25\cdot3}=5\sqrt{3}\).

Hope this helps.