Question

The width of two boards is \[8.125{\text{ inches}}\] and \[8\dfrac{1}{8}{\text{ inches}}\]. Which number sentence correctly compares the width of these two boards?
a) \[8.125 < 8\dfrac{1}{8}\]
b) \[8.125 = 8\dfrac{1}{8}\]
c) \[8.125 > 8\dfrac{1}{8}\]
d) none of these

Answer 1

Hint: To solve this, we need to compare the widths of the two boards. But in the question the widths are not given in the same format so, we cannot compare them. To compare we will first convert them in the same format i.e. we can convert the fraction into decimal and then check which one is smaller and which one is greater or whether they are equal or not.

Complete answer:
We have one of the widths as \[8.125{\text{ inches}}\] and the other as \[8\dfrac{1}{8}{\text{ inches}}\]. We will convert the latter one into the format in which the former one is given.
Now we can write;
\[8\dfrac{1}{8}{\text{ inches }} = \left( {8 + \dfrac{1}{8}} \right){\text{ inches}}\]
On dividing and adding we get;
\[ \Rightarrow 8\dfrac{1}{8}{\text{ inches }} = \left( {8 + 0.125} \right){\text{ inches}}\]
\[ \Rightarrow 8\dfrac{1}{8}{\text{ inches }} = 8.125{\text{ inches}}\]
Now we can see that both the widths given have the same measurement. So, they are equal.

Therefore, the correct option is b

Note: One thing to note here is that in this question the units of the two widths are the same but the way in which the magnitudes are written is different. In some other questions, the units may be different. There we need to convert both of them into the same unit and then we can compare. Another point to note is that we have converted \[8\dfrac{1}{8}{\text{ inches}}\] into the decimal format, but we can also compare the given widths by converting the width which is in the decimal format into the fraction format. Both of these processes are true and will give the same result.