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 into simple fractions and compare them:

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

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

0.25 is divided 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

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: $0.661\text{ }0.662\text{ }0.663\text{ }0.664\text{ }0.665\text{ }0.666\text{ }0.667\text{ }0.668,\text{ }0.669$.

Now if we look at the possible answers and compare them to our number range, we can deduce that the answer is 0.665 as it appears in both.

Let's look at the number 0.41 and we can see that it equals 0.41

$0.41=0.41$

Therefore this is not the correct answer.

Let's look at the number 0.405, the number after the decimal point is identical meaning 4 equals 4 but the number 0 is less than 1

0.405 < 0.41

Therefore this is not the correct answer.

Let's look at the number 0.4, we'll add 0 to it and get the number 0.40 now let's look at the numbers after the decimal point, 4 equals 4 and 0 is less than 1

0.40 < 0.41

Therefore this is not the correct answer.

Let's look at the number 0.42, we can see that the number after the decimal point is 4, and the number after it is 2. Since 2 is greater than 1

0.42 > 0.41

Therefore this is the correct answer

To determine the correct answer, let's first add 0 to the number 0.31 in the following way:

$0.31=0.310$

In other words, we need to find a number that is greater than 310

Let's look at the answers:

0.311 - Since the thousandths digit is 1 and 1 is greater than 0, this is the correct answer.

0.309 - Since the hundredths digit is 0 and 0 is less than 1, this is not the correct answer.

0.3 - If we add two zeros we get the number 0.300, since the hundredths digit is 0 and 0 is less than 1, this is not the correct answer.

0.31 - If we add 0 to the number we get 0.310, since the thousandths digit is 0 and 0 is less than 1, this is not 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.