Comparing Decimal Fractions - Examples, Exercises and Solutions

We will add 0 to the number 0.5 in the following way:

$0.5=0.50$

And we will discover that the numbers are not identical

We will add 0 to the number 0.1 in the following way:

$0.1=0.10$

And we will discover that the numbers are indeed identical

We will add 0 to the number 0.2 in the following way:

$0.2=0.20$

And we will discover that the numbers are not identical

Let's observe the numbers after the decimal point.

Due to the fact that 23 and 32 are not identical, the numbers cannot be considered as the same number.

We will add 0 to the number 0.25 in the following way:

$0.25=0.250$

And we will discover that the numbers are identical

We will add 0 to the number 0.5 in the following way:

$0.5=0.50$

And we will discover that the numbers are identical

We will add 0 to the number 0.6 in the following way:

$0.6=0.60$

And we will discover that the numbers are identical

We will add 0 to the number 0.8 in the following way:

$0.8=0.80$

And we will discover that the numbers are not identical

Let's convert the decimal numbers into simple fractions and compare them:

0.24 is divisible by 100 because there are two digits after the decimal point, therefore:

$0.24=\frac{24}{100}$

0.25 is divisible by 100 because there are two digits after the decimal point, therefore:

$0.25=\frac{25}{100}$

Let's now compare the numbers in the numerator:

\frac{25}{100}>\frac{24}{100}

Therefore, the larger number is 0.25.

We will add 0 to the number 0.02 in the following way:

$0.02=0.020$

And we will discover that the numbers are not identical

Just as the number 45 is not equal to 445, nor is the number 0.45 equal to 0.445—even though their values are relatively close.

This can be seen more clearly in the form of a regular fraction:

45/100 is not equal to 445/1000

First, let's convert 0.8 into a simple fraction.

Since there is only one number after the decimal point, we can divide by 10 as follows:

$0.8=\frac{8}{10}$

Let's simplify the fraction so that we have two fractions with the same denominator:

$\frac{8:2}{10:2}=\frac{4}{5}$

Now we can compare and see that:

$\frac{4}{5}=\frac{4}{5}$

First, we will convert the simple fraction to a decimal fraction.

We will write the numerator of the fraction in decimal form and divide by 10 as follows:

$12=12.0$

$\frac{12.0}{10}=1.2$

Now we can compare the two fractions and see that:

$\frac{12}{10}=1.2$

First, let's convert 0.3 to a simple fraction.

Since there is only one number after the decimal point, the number divides by 10 as follows:

$0.3=\frac{3}{10}$

Now we have two simple fractions with different denominators.

To compare them, note that the smallest common denominator between them is 30.

We'll multiply each one to reach the common denominator as follows:

$\frac{1}{3}\times\frac{10}{10}=\frac{10}{30}$

$\frac{3}{10}\times\frac{3}{3}=\frac{9}{30}$

Now we can compare the two fractions and see that:

\frac{10}{30}>\frac{9}{30}

First, let's convert 0.6 to a simple fraction.

Since there is only one digit after the decimal point, the number is divided by 10 as follows:

$0.6=\frac{6}{10}$

Let's reduce the fraction:

$\frac{6:2}{10:2}=\frac{3}{5}$

Now we have two simple fractions with different denominators.

To compare them, note that the smallest common denominator between them is 15.

We'll multiply each one to reach the common denominator as follows:

$\frac{2}{3}\times\frac{5}{5}=\frac{10}{15}$

$\frac{3}{5}\times\frac{3}{3}=\frac{9}{15}$

Now we can compare the two fractions and see that:

\frac{10}{15}>\frac{9}{15}