Question

Which of the following numbers is smaller?
7 or 8.5

Answer 1

Hint: We solve this problem first by converting the given numbers into fractions of equal denominators. Then we check the number which is smaller.
We have the condition that in a fraction if the denominator is the same then the fraction having less number in the numerator is the smallest among them.

Complete step by step answer:
We are given that the two numbers as 7 and 8.5
Let us consider the number 7 as
\[\Rightarrow x=7\]
Now, let us convert the decimal number to fraction then we get
\[\Rightarrow x=\dfrac{7}{1}\]
Now, let us consider the number 8.5 as
\[\Rightarrow y=8.5\]
Now, let us convert the decimal number to fraction then we get
\[\Rightarrow y=\dfrac{85}{10}\]
Here, we can see that the denominators in the given two numbers are different
Now, let us convert them into the same denominator.
Here the denominator in the second number is 10 and that of the first number is 1

Now, by multiplying the first number with 10 in numerator and denominator then we get
\[\begin{align}
  & \Rightarrow x=\dfrac{7\times 10}{1\times 10} \\
 & \Rightarrow x=\dfrac{70}{10} \\
\end{align}\]
Here we can see that the denominators in both the numbers are equal
We know that the condition that in a fraction if the denominator is the same then the fraction having less number in the numerator is the smallest among them.
By using the above condition we can see that number 70 is less than 85 then we get
\[\begin{align}
  & \Rightarrow \dfrac{70}{10} < \dfrac{85}{10} \\
 & \Rightarrow x < y \\
\end{align}\]
By substituting the original values in above equation then we get
\[\Rightarrow 7 < 8.5\]
Therefore, we can conclude that the number 7 is less than 8.5

Note:
We can solve this problem in other methods by checking the digits.
We have the condition that while comparing the digits from the left side the number having the less digit will be the smallest number.
We are given that 7 and 8.5
Now, let us compare the first digits from left in both numbers.
Here, we can see that the first digit in the first number is 7 and the first digit in the second number is 8
By comparing the digits we get
\[\Rightarrow 7 < 8\]
Therefore we can conclude that the number 7 is less than 8.5