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.
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.
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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