Comparing Decimal Fractions - Examples, Exercises and Solutions

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 0.8 in the following way:

$0.8=0.80$

And we will discover that the numbers are not 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 not identical

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

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 0.6 in the following way:

$0.6=0.60$

And we will discover that the numbers are identical

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

$0.5=0.50$

And we will discover that the numbers are identical

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

$0.2=0.20$

And we will discover that the numbers are not identical

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

0.24 is divided by 100 because there are two digits after the decimal point, so:

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

0.25 is divided by 100 because there are two digits after the decimal point, so:

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

Let's 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, similarly 0.45 is not equal to 0.445,

even though their values are relatively very close.

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

45/100 is not equal to 445/1000

In order to discover our range of numbers, we will first add 0 to both numbers as follows:

$0.66=0.660$

$0.67=0.670$

This means our number will be in the range between 0.660 and 0.670

The numbers that exist in this range are: $0.661\text{ }0.662\text{ }0.663\text{ }0.664\text{ }0.665\text{ }0.666\text{ }0.667\text{ }0.668,\text{ }0.669$

We will look at the answers and see that 0.665 is within this range and therefore this is the correct answer

To determine which answer is correct, let's compare the answers to the number 0.751 and find out which one is larger:

Let's look at the answers:

0.752 - Since the thousandths digit is 2 and 2 is greater than 1, this is the correct answer.

0.749 - Since the hundredths digit is 4 and 4 is less than 5, this is not the correct answer.

0.75 - If we add 0 we get the number 0.750, since the thousandths digit is 0 and 0 is less than 1, this is not the correct answer.

0.751 - Since both numbers are equal to each other, this is not the correct answer.

To determine which answer is correct, let's compare the answers and find out which one is less than 0.91:

Let's look at the answers:

0.9 - If we add 0 we get the number 0.90, since the hundredths digit is 0 and 0 is less than 1, this is the correct answer.

0.93 - Since the hundredths digit is 3 and 3 is greater than 1, this is not the correct answer.

0.92 - Since the hundredths digit is 2 and 2 is greater than 1, this is not the correct answer.

0.91 - Since both numbers are equal to each other, this is not the correct answer.

To determine which answer is correct, let's compare the answers to 0.65 and find out which one is larger:

Let's look at the answers:

0.66 - Since the hundredths digit is 6 and 6 is greater than 5, this is the correct answer.

0.749 - In this case, we'll add 0 to our number and compare between 0.650 and 0.749. Since the hundredths digit is 4 and 4 is less than 5, this is not the correct answer.

0.65 - Since both numbers are equal to each other, this is not the correct answer.

0.64 - Since the hundredths digit is 4 and 4 is less than 5, this is not the correct answer.