Tenths as Decimals

Reviewed by the Helping with Math Team · Updated 10 October 2026

Introduction

The word decimal comes from the Latin word “Decem” meaning 10. A decimal number can be defined as a number whose complete part and the fractional part are separated by a decimal point. Before we learn what we mean by a tenth of decimal it is important to recall the place value system of decimals that defines the position of a tenth in a decimal number.

Place value system of decimals

We know that each place in the place value table has a value ten times the value of the next place on its right. In other words, the value of a place is one-tenth of the value of the next place on its left. We observe that if one digit moves one place left to right its value becomes one-tenth ($\frac{1}{10}$ ) of its previous value and when it moves two places left to right its value comes one-hundredth ( $\frac{1}{100}$ ) of its previous term and so on. Therefore, if we wish to move beyond ones place which is the case of decimals, we will have to extend the place value table by introducing the places of tenths ($\frac{1}{10}$ ), hundredths ($\frac{1}{100}$ ), thousandths ( $\frac{1}{1000}$ ) and so on.

Therefore, the place value table in case of a decimal number will be of the form –

For example, the decimal number 257.32 in the place value system will be written as –

A decimal or a decimal number may contain a whole number part and a decimal part. The following table shows the whole number part and the decimal part of some decimals –

Now, how do we read the decimals using the place value system? Let us find out.

Reading the Decimal Numbers using the Place Value System

In order to read decimals, the following steps are used –

1. Read the whole number part
2. Read the decimal point as point
3. Read the number to the right of the decimal point. For example, 14.35 will be read as Fourteen point three five. Alternatively, the number to the right of the decimal point can also be read by reading the number to the right of the decimal point and naming the place value of the last digit. For instance, the number 8.527 can also be read as eight and five hundred twenty seven thousandths.

What are tenths in a decimal?

Consider the following figure. It is divided into ten equal parts and one part is shaded. The shaded part represents one-tenth of the whole figure. It is written as $\frac{1}{10}$. $\frac{1}{10}$ is also written as 0.1 which is read as “ point one “ or “ decimal one “.

Thus the fraction $\frac{1}{10}$ is called one-tenth and is written as 0.1.

Also, 1 one = 10 tenths.

Consider another figure. The below figure is divided into ten equal parts and three parts are shaded. The shaded parts represent three-tenths of the whole figure. It is written as $\frac{3}{10}$. $\frac{3}{10}$ is also written as 0.3 which is read as “ point three “ or “ decimal three “.

Thus the fraction $\frac{3}{10}$ is called three tenth and is written as 0.3.

Also, consider the below figure. The below figure is divided into ten equal parts and six parts are shaded. The shaded parts represent six-tenths of the whole figure. It is written as $\frac{6}{10}$. $\frac{6}{10}$ is also written as 0.6 which is read as “ point six “ or “ decimal six “.

Thus the fraction $\frac{6}{10}$ is called six-tenth and is written as 0.6.

Similarly, $\frac{2}{10}$, $\frac{4}{10}$, $\frac{5}{10}$, $\frac{7}{10}$, $\frac{8}{10}$ and $\frac{9}{10}$ are called 2 tenths, 4 tenths, 5 tenths, 7 tenths, 8 tenths and 9 tenths, and are written 0.2, 0.4, 0.5, 0.7, 0.8 and 0.9.

Thus we have,

$\frac{1}{10}$ = 0.1 and is called one-tenth or 1 tenth

$\frac{2}{10}$ = 0.2 and is called two-tenths or 2 tenths

$\frac{3}{10}$ = 0.3 and is called three-tenths or 3 tenths

$\frac{4}{10}$ = 0.4 and is called four-tenths or 4 tenths

$\frac{5}{10}$ = 0.5 and is called five-tenths or 5 tenths

$\frac{6}{10}$ = 0.6 and is called six-tenths or 6 tenths

$\frac{7}{10}$ = 0.7 and is called seven-tenths or 7 tenths

$\frac{8}{10}$ = 0.8 and is called eight-tenths or 8 tenths

$\frac{9}{10}$ = 0.9 and is called nine-tenths or 9 tenths

$\frac{10}{10}$ = 1 and is called ten-tenths or 10 tenths

Tenths

4

4 tenths = 4/10 = 0.4
Read it as “zero point four”.

Also, $\frac{11}{10}$ = 11 tenths = 10 tenths + 1 tenths = 1 + $\frac{1}{10}$ = 1 + 0.1 = 1.1

$\frac{12}{10}$ = 12 tenths = 10 tenths + 2 tenths = 1 + $\frac{2}{10}$ = 1 + 0.2 = 1.2

$\frac{13}{10}$ = 13 tenths = 10 tenths + 3 tenths = 1 + $\frac{3}{10}$ = 1 + 0.3 = 1.3

Similarly, we have

$\frac{20}{10}$ = 20 tenths = 10 tenths + 10 tenths = 1 + 1 = 2

$\frac{21}{10}$ = 21 tenths = 20 tenths + 1 tenths = 2 + $\frac{1}{10}$ = 2 + 0.1 = 2.1

$\frac{22}{10}$ = 22 tenths = 20 tenths + 2 tenths = 2 + $\frac{2}{10}$ = 2 + 0.2 = 2.2

Thus a fraction of the form $\frac{Number}{10}$ is written as decimal obtained by putting decimal point by leaving one right-most digit.

For example, $\frac{325}{10}$ = 32.5 while $\frac{5894}{10}$ = 589.4

Let us understand it through an example.

Example Write each of the following as decimals

1. Five ones and four tenths
2. Twenty and one tenths

Solution We have been given the following and we need to write them as decimals. Let us do them one by one

1. Five ones and four tenths

Note that the whole value of the given decimal is 5 and the decimal part is four tenths. Therefore, we will proceed in the same manner as we defined different tenths above.

We will get,

Five ones and four tenths = 5 ones + 4 tenths = 5 + $\frac{4}{10}$ = 5 + 0.4 = 5.4

Hence, Five ones and four tenths In decimal form will be 5.4.

2. Twenty and one tenths

Note that the whole value of the given decimal is 20 and the decimal part is one-tenths. Therefore, we will proceed in the same manner as we defined different tenths above.

We will get,

Twenty ones and one tenths = 20 ones + 1 tenths = 20 + $\frac{1}{10}$ = 20 + 0.1 = 20.1

Hence, Twenty ones and one tenths in decimal form will be 20.1.

Let us take another example.

Example Write each of the following as decimals

1. 20 + 7 + $\frac{3}{10}$
2. 500 + 3 + $\frac{7}{10}$

Solution We have been given an expanded form of two numbers and we are required to find the corresponding decimal number. Let us do them one by one.

1. 20 + 7 + $\frac{3}{10}$

We can see that there are two whole numbers and one fractional number.

Note that the whole values of the given decimal are 20 and 7 and the decimal part is three tenths. Therefore, we will proceed in the same manner as we defined different tenths above.

We will get,

20 + 7 + $\frac{3}{10}$ = 20 + 7 + 0.3 = 27.3

2. 500 + 3 + $\frac{7}{10}$

We can see that there are two whole numbers and one fractional number.

Note that the whole values of the given decimal are 500 and 3 and the decimal part is seven tenths. Therefore, we will proceed in the same manner as we defined different tenths above.

We will get,

500 + 3 + $\frac{7}{10}$ = 500 + 3 + 0.7 = 503.7

Let us now see how to plot the tenths of a decimal on a number line.

Tenths on a number line

Before we learn how to represent a tenth on a number let us recall what we understand by the term number line.

What is a number line?

A number line is a straight horizontal line with numbers placed at even intervals that provides a visual representation of numbers. The basic operations of addition, subtraction, multiplication and division can all be performed on a number line. The numbers increase as we move towards the right side of a number line while they decrease as we move left.

Representation on a Number Line

Above is a visual representation of a standard number line. As is clearly visible, as we move from left to right, there is an increase in the value of numbers while it decreases when we move from right to left.

We already know how to represent fractions on a number line. Let us now represent tenths of a decimal on a number line. We can understand this by an example.

Let us represent 0.4 on a number line. We can clearly see that there are 4 tenths in 0.4. Therefore in order to represent 0.4 on a number line we will divide the unit length between 0 and 1 into 10 equal parts and take 4 parts as shown below –

Now, we can know that 0.4 in fraction form is equal to 4/10. Hence we will mark 4/10 as 0.4 which is our desired mark on the number line.

The steps that we used above to represent a tenth on a number line can be summarized as –

1. We draw a number line between 0 and 1.
2. We then draw 9 marks between 0 and 1, dividing the distance into 10 equal parts.
3. Now, one whole divided into 10 parts is equal to $\frac{1}{10}$.
4. $\frac{1}{10}$ in decimal form is equal to 0.1.
5. At each new line we are adding $\frac{1}{10}$ or 0.1.
6. So, between 0 and 1 we have 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9. Similarly, between 1 and 2 we have 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8 and 1.9.
7. We can also say that the line representing $\frac{1}{2}$ or 0.5 is the half way mark between 0 and 1. Similarly, the line representing $1\frac{5}{10}$ or 1.5 is the half way mark between 1 and 2.
8. Ten tenths is equal to one whole.

Now let us go through some solved examples on tenth of a decimal.

Solved Examples

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