Comparing Quantities

Example 1:

Which number among $\frac{1}{4}$ and $0.3$ is greater?

Here, one number is a fraction and the other is a decimal.

To make the comparison easier, convert the fraction into a decimal. Divide the numerator by the denominator.

So, $\frac{1}{4}=0.25$ .

Thus, we have two decimals, $0.25$ and $0.3$ . Since $0.3>0.25$ , the decimal $0.3$ is greater than the fraction $\frac{1}{4}$ .

Example 2:

Fill in the blanks with $<,>\text{ or }=$ .

$0.4\boxed{\underset{\_}{}}45\%$

Here, one number is a decimal and the other is a percent.

To make the comparison easier, convert the percent into a decimal.

Remember that a percent is really just a special way of expressing a fraction as a number out of $100$ . Then, $45\%=\frac{45}{100}=0.45$ .

So, $45\%=0.45$ .

Thus, we have two decimals, $0.45$ and $0.4$ . Since $0.4<0.45$ , $0.4\boxed{<}45\%$ .

Example 3:

Jordan finished $3$ out of $8$ homework problems. Kate is done with $40\%$ of her homework problems. Who has done a greater percentage of homework?

Here, one number is a fraction and the other is a decimal.

To make the comparison easier, convert the fraction into percent. First, divide the numerator by the denominator.

So, $\frac{3}{8}=0.375$ . Now, to convert to percent , multiply the decimal by $100$ .

$0.375\times 100=37.5$

That is, $\frac{3}{8}=37.5\%$ .

Since $40\%>37.5\%$ , Kate has done a greater percentage of homework.