Question

I need help with finding out what type of number something is. like if its a Rational number or an Integer or Irrational number. stuff like that! (Algebra 1)

Answer 1

ill help :)

Answer 2

first off we have the natural numbers, these are just the normal counting numbers:

1,2,3,4,5,6,......

Answer 3

then we have the integers, these are the natural numbers AND the negative whole numbers:

...,-5,-4,-3,-3,-1,0,1,2,3,4,5,..

Answer 4

then we have the rational numbers, these are numbers that we get when we divide integers by each other

for example 1/2 , 3/5 , -2/3 are all rational numbers. remember all integers are rationals because we can write them like this: \[5= \frac{5}{1}\]

Answer 5

alrighty! I need to know about 6 different kinds of numbers! Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, and Real Numbers

Answer 6

ok :D so far i have done naturals, integers, and rationals. "whole numbers" can mean different things depending on what you're talking about, when i think of whole numbers i think of integers, and they're basically the same thing

Answer 7

Irrational Numbers are any numbers you cant write as a ratio of integers. for example the square root of 2 cannot be written as a fraction.

Answer 8

well my teacher said that almost all these things can equal one another.Like a natural number can be a whole number and a whole number can be an integer that can be a rational number which is a real number

Answer 9

ill draw a diagram that might help with that bit

Answer 10

think of this circle as the Real Numbers. probably all numbers you've seen are Real Numbers, there are other types of numbers that aren't real, but i wont talk about them (unless you want me to after this)

Answer 11

lets split the circle to show the rationals and the irrationals:

Answer 12

here is where the integers live:

Answer 13

and the naturals:

Answer 14

thats kinda like what she made for us

Answer 15

nice! yeah thats much better than my drawing

Answer 16

is there anything more you want me to explain about it?

Answer 17

That actually helps alot!
So fractions are always an integer and irrationals are always a square root?

Answer 18

all integers are rational (fractions), rationals (fractions) aren't necessarily integers.

eg 1/2 is NOT an integer, but 6 IS a rational

Answer 19

how is 6 rational?

Answer 20

because 6 can be written like this :

\[\frac{6}{1}\]

Answer 21

irrationals dont have to be a square root, for example pi is irrational

Answer 22

okay but if it is a squareroot is it irrational?

Answer 23

only some (i know, this is probably a bit frustrating)

square roots of numbers that AREN'T square are irrational

eg

\[\sqrt{2} \text{ is, but } \sqrt{4} \text{ isn't}\] because the square root of 4 is 2

Answer 24

also other roots can be irrational:

\[\sqrt[3]{2}\]

Answer 25

okay thanksss