Ordering Fractions and Decimals

• If fractions and decimals are to be compared and ordered in either increasing or decreasing order, all of them must be converted either to fractions or to decimals.

• Fractions and decimals cannot be compared directly. It is like comparing apples and oranges. They are of a different kind and cannot be compared.

• So, all quantities must be either in fraction form or in decimal form to compare.

• It is found that it is more convenient to convert the given quantities to decimals and then compare and order them.

Compare using >, <, =

$0.5 \: \square \: \frac{5}{100}$

Solution

Step 1:

Converting the fraction $\frac{5}{100}$ into a decimal, we move the decimal two places to left and get $\frac{5}{100} = 0.05$

Step 2:

Now both the quantities are in decimal form and can be compared

Comparing $0.5 \: \square \: \frac{5}{100}$

Step 3:

Using place values to compare; five tenths are greater than five hundredths So, 0.5 > 0.05

Step 4:

So, $0.5 > \frac{5}{100}$

Compare using >, <, =

$0.72 \: \square \: \frac{8}{10}$

Solution

Step 1:

Converting the fraction $\frac{8}{10}$ into a decimal, we move the decimal one place to left and get $\frac{8}{10} = 0.8 = 0.80$

Step 2:

Now both the quantities are in decimal form and can be compared

Comparing 0.72 ☐ 0.80

Step 3:

Using decimal place values to compare; seventy-two hundredths are less than eight tenths or eighty hundredths.

So, 0.72 < 0.80

Step 4:

So, $0.72 < \frac{8}{10}$