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

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

Answer: 4<√18<19/4

2. Now we can order the rest easily

Answer: -2.74<2.76<4<√18<19/4