Question

Write any three rational numbers between the two numbers given below.
5.2 and 5.3

Answer 1

Hint: First of all, take the numbers that are 5.2 and 5.3 and use \[x=\dfrac{a+b}{2}\] to find the rational number x between a = 5.2 and b = 5.3. Now keep using it in between ‘a’ and ‘x’ and ‘x’ and ‘b’ to find two more rational numbers between a and b.

Complete step-by-step answer:
In this question, we have to find three rational numbers between 5.2 and 5.3. Now, we know that to find the rational number x between any two rational numbers a and b, we use
\[x=\dfrac{a+b}{2}....\left( i \right)\]
Therefore, to find the rational number x between 5.2 and 5.3, using equation (i), we get,
\[x=\dfrac{5.2+5.3}{2}=\dfrac{10.5}{2}\]
\[x=5.25\]
Therefore, we get, first rational number between 5.2 and 5. 3 as 5.25.
Now, if we find the rational number between 5.2 and 5.25, it will also lie between 5.2 and 5.3. So by again using equation (i), we get the next rational number y as:
\[y=\dfrac{5.2+5.25}{2}=\dfrac{10.45}{2}\]
\[y=5.225\]
Therefore, we get the second rational number between 5.2 and 5.3 as 5.225.
Now, if we find a rational number between 5.25 and 5.3, it will also lie between 5.2 and 5.3. So, by again using equation (i), we get the next rational number z as:
\[z=\dfrac{5.25+5.3}{2}=\dfrac{10.55}{2}\]
\[z=5.275\]
Therefore, we get the third rational number between 5.2 and 5.3 as 5.275.
Hence, the three rational numbers between 5.2 and 5.3 are 5.25, 5.225, and 5.275.

Note: In this question, we can cross-check our answers by examining if all the three numbers that are 5.25, 5.225, and 5.275 are lesser than 5.3 and greater than 5.2 or not. As we can see that 5.2 < 5.25, 5.225, 5.275 < 5.3, hence our answer is correct. Also, take special care while dividing the numbers involving decimals because many students make a mistake in that.