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 pke 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, $0.72 < frac{8}{10}$