Question

Is the number rational or irrational?
Column A Column B
1. A. rational
3/7
B. irrational
2.
---
0.78

3.
square root of 7 over 9 end root

4.
5 pi

Answer 1

Pi is irr....

Answer 2

1. a
2.b
3.b i think
4.?
5 b

Answer 3

if it can be written as an a/b
where a and b are both integers (and a is not 0)
then it is rational
so this means any decimal that terminates or repeats is rational


if it isn't rational and it is a real number, then it is irrational
so things like pi, sqrt(2), sqrt(pi), sqrt(91), pi^2-1 are irrational numbers

Answer 4

why do you say .78 is irrational?

Answer 5

cuz its a decimal

Answer 6

\[.78=\frac{78}{100}\]

Answer 7

decimals that terminate or repeat can be written as fractions when you have integer over integer

Answer 8

\[.12121212.... \text{ is also rational } \\ \text{ Let } x=.12121212.... \\100x=12.12121212.... \\ \text{ now subtract equations } \\ 100x-x=12.12121212.....-.1212121212.... \\ 99x=12 \\ x=\frac{12}{99}\]
so .121212121212... can be written as 12/99
this again is an integer over an integer
so therefore .12121212.... is rational