# Real Numbers

### Overview ### Real Number Types

Natural Whole Integers Rational Irrational Real Imaginary Complex  ### Comparing Real Numbers

Q: When comparing real number you will most likely be given Fractions, Decimals, and Square Roots

A: Unless these numbers are very simple you should convert the fractions and square roots to decimals and compare these decimals

Example Problems

Order the Following from least to greatest:

1 ) -1.6, - √ 8 , 2.3, 4.3, 17

2 ) 4, 2.76, 19/4, √18, -2.74

### Example Problem Solutions

Question 1:

1. First we can estimate -√8

√4<√8<√9 --> 2<√8<3 --> -3>-√8>-2

Therefore, -√8 is clearly less than -1.6

2. Then we can use a calculator or solver √17 by hand (See Square Roots Lesson)

√17 = 4.123

Therefore, 4.3 is clearly greater than 4.123

3.Now we can see that the order is the following

-8<1.6<2.3<√17<4.3

Question 2:

1. First we should compare 4, 19/4, and √18

19/4 = 4.75

16<√18<25 --> 4<√18<5

You can assume that 18 is less than 19/4 because 18 is closer to 4 or 16