# ORDERING REAL NUMBERS ON A NUMBER LINE WORKSHEET

## About "Ordering real numbers on a number line worksheet"

Ordering real numbers on a number line worksheet :

Worksheet on ordering real numbers on a number line is much useful to the students who would like to have better understanding on real numbers.

## Ordering real numbers on a number line worksheet - Questions

1.  Order √22, π+1 and 4 1/2 on a number line. Then list them in the order from least to greatest.

2.   Order π², 10 and √75 on a number line. Then list them in the order from least to greatest.

## Ordering real numbers on a number line worksheet - Answers

Question 1 :

Order √22, π+1 and 4 1/2 on a number line. Then list them in the order from least to greatest.

Solution :

Step 1 :

First approximate √22.

√22 is between 4 and 5. Since we don’t know where it falls between 4 and 5, we need to find a better estimate for √22.

So that we can compare it to 4 1/2.

Since 22 is closer to 25 than 16, use squares of numbers between 4.5 and 5 to find a better estimate of √22.

4.5²  =  20.25

4.6²  =  21.16

4.7²  =  22.09

4.8²  =  23.04

Since 4.7²  =  22.09, an approximate value for  √22 is 4.7.

That is,

√22 ≈  4.7 -------- (1)

Step 2 :

An approximate value of π is 3.14. So an approximate value of π+1 is 4.14.

That is,

π+1 ≈  4.14 -------- (2)

Step 3 :

The value of 4 1/2 is 4.5.

That is,

4 1/2  =  4.5 -------- (3)

Step 4 :

Plot  √22, π+1 and 4 1/2 on a number line.

Step 5 :

Read the numbers from left to right to list them in order from least to greatest..

π+1, 4 1/2, √22

Question 2 :

Order π², 10 and √75 on a number line. Then list them in the order from least to greatest.

Solution :

Step 1 :

An approximate value of π is 3.14. So an approximate value of π² is 9.86.

That is,

π² ≈  9.86 -------- (2)

Step 2 :

First approximate √75.

√75 is between 8 and 9.

Since we do not know the exact value of √75, we have to mark √75 on a number line at somewhere between 8 and 9.

Step 3 :

Now, plot π², 10 and √75 on a number line

Step 4 :

Read the numbers from left to right to list them in order from least to greatest..

√75,  π², 10

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