#### Question

# How do you determine if a number is rational or irrational?

I'm having trouble with this, I have

3.47 and this one has a line over the 47 because it is non-ending

2.346

2.26

√625

√48

π/3

How do you know which one's are rational and irrational?

#### Answer

rational numbers are any numbers that can be expressed as the ratio of 2 integers

Irrational numbers are numbers that cannot be expressed as the ratio of 2 integers

3.47474747474....

Let 3.47474747... = x

x = 3.4747474747

Multiply both sides by 100

100x = 347.4747474747

Subtract the first equation from the second equation

100x - x = 347.47474747... - 3.4747474747...

99x = (347 - 3) + (0.47474747... - 0.4747474747...)

99x = 344 + 0

99x = 344

x = 344 / 99

Rational

2.346 => (2.346 * 1000) / 1000 = 2346 / 1000

Rational

2.26 = (2.26 * 100) / 100 = 226 / 100

Rational

sqrt(625) = sqrt(25 * 25) = 25

Rational

sqrt(48) = sqrt(16 * 3) = 4 * sqrt(3)

The square root of 3 is irrational, so 4 * sqrt(3) is also irrational.

pi/3 is irrational because pi is not a rational number

3.47 and this one has a line over the 47 because it is non-ending

rational

2.346

rational

2.26

rational

√625

rational

√48

irrational

π/3

irrational

3.47474747... = 3 47/99 rational

2.346 = 2346/1000 rational

2.26 = 236/100 rational

√625 = 25 rational

√48 = 4√3 irrational

π/3 = irrational

Irrational numbers don't stop, they go till infinity. A few examples:

Rational Numbers are allowed to go till infinity too but only if the digits are reoccuring:

6.53

9

0.356

0.454545454545...

5.191919191919...

Irrational Numbers:

pi

0.264636284...

1.2834663...

root 2