Decimal Numbers: Definition, Types, Properties, Conversions

Decimal Numbers: A decimal number is one in which a decimal point separates the full number and fractional parts. For example, let us say you are going to take chocolate ice cream. The vendor tells you that the price of ice cream is \(₹20\) and \(50\,{\rm{paise}}\). Now, if you want to express this whole amount in one figure, you will say that the price of the chocolate ice cream is \(₹20.50\).

There are many such real-life situations in which you might be using decimals without even realizing it. Let us learn about decimal numbers in this article.

What are Decimal Numbers?

We all love pizza, don’t we? Look at the figure below. We have two and a half pizzas. The same has been expressed as a fraction and as a decimal.

Every decimal number has two parts: The whole number part and the decimal (fractional) part.

So, in short, we can define decimal numbers as a number that has a decimal point followed by digits that show the fractional part. The number of digits in the decimal part determines the number of decimal places.

For example, the number of decimal places in \(2.4\) is \(1,\) in \(3.24\) is \(2\) and in \(0.0009\) is \(4.\)

Types of Decimal Numbers

Decimal numbers are classified into many types. They are
1. Terminating Decimal Numbers: The terminating decimal numbers have a finite number of digits just after the decimal point. Such a type of decimal number is known as an exact decimal number. For example,\(34.9807,55.5\)
2. Non-Terminating Decimal Numbers: Non-terminating decimal numbers are the numbers where the digits after the decimal point repeat endlessly.
3. Recurring Decimal Numbers: Recurring decimal numbers are those numbers that have an infinite number of digits after the decimal point, but these digits are repeated at regular intervals in some pattern. For example, \(9.505050\).
4. Non-Recurring Decimal Numbers: Non-recurring decimal numbers are the non-terminating/ non-repeating decimal numbers. They have an infinite number of digits at their decimal places, and also, their decimal digits do not follow any specific order. For example, \(7009.97658….\)

Representation and Examples of Decimal Numbers

Let us take an example of a decimal number \(7.48\), in which \(7\) is the whole number, while \(48\) is the decimal part. 

Decimals are based on the preceding powers of \(10\) Thus, as we move from left to right, the value of digits gets divided by \(10\) the decimal place value determines the tenths, hundredths, and thousandths. A tenth means one-tenth or \(\frac{1}{{10}},\) in decimal form, it is \(0.1\) Hundredth means \(\frac{1}{{100}},\) in decimal form,\(0.01\)Thousandths means \(\frac{1}{{1000}},\) in decimal form, it is \(0.001\) and so on.

Here is an example of how to convert the fractional part into decimals.

We can represent the tenths, hundredths, and thousandths on a number line. To represent tenths, we divide the distance between each whole number on a number line into \(10\) equal parts where each part represents a tenth. To represent hundredths, we partition the distance between each whole number on a number line into \(100\) equal parts and so on.

Decimal Number in Words

Here are the simple steps to follow when writing decimal in words. To read and write decimals, use the following steps:

1. First, read the digits to the left of the decimal point as a whole number.
2. Read point for the decimal point.
3. Read the digits to the right of the decimal point as a single whole number.

Let us understand how to read decimal numbers in words with the help of a couple of examples.

1. \(0.457\,\, = \) Zero point four five seven
2. \(15.15\,\, = \) Fifteen point one five
3. \(200.009\, = \) Two hundred point zero zero nine

Another way to write decimals in words is

1. \(25.578\,\, = \) Twenty-five and five hundred seventy-eight thousandths.
2. \(700.24\,\, = \) Seven hundred and twenty-four hundredths.
3. \(0.005\, = \) Five thousandths

Place Value of Decimal Numbers

The place value system is used to define the position of a digit in a number which helps to determine its value. When we write specific numbers, the position of each digit is important. The power of \(10\) can be found using the following place value chart:

The digits present in the left of the decimal point are multiplied with the positive powers of \(10\) in increasing order from right to left.

The digits present to the right of the decimal point are multiplied with the negative powers of \(10\) in increasing order from left to right.

Let’s understand with the help of an example.

Consider the decimal number \(3684.26\).

Let us arrange the given decimal number according to its place value, as shown below.

The decimal expansion of the number is \(\left\{ {(3 \times 1000) + (6 \times 100) + (8 \times 10) + (4 \times 1) + (6 \times 0.1) + (6 \times 0.001)} \right\}\)

Decimal Numbers to Fractions Conversion

We can easily perform the conversion of decimal number to fraction or fraction to decimal number. Now, we will discuss both the conversion methods below:

Decimal to Fraction Conversion

To convert a decimal number into a fraction, we go through the following steps:

1. Remove the decimal point from the decimal number. The number obtained becomes the numerator of the fraction.
2. Write denominator as \(1\) followed by as many zeros as the number of decimal places in the given decimal number.
3. Simplify the fraction, if possible

For example \(3.9\, = \,\frac{{39}}{{10}},45.451\, = \,\frac{{45451}}{{1000}}\).

Fraction to Decimal Number Conversion

To convert a fraction whose denominator is not a factor of \(10,100,1000\) and so on into a decimal number, we go through the following steps:

1. Convert the given fraction into an equivalent common fraction by changing its denominator into \(10\) or multiples of \(10\).
2. Convert the obtained fraction into a decimal number. For example, \(\frac{2}{5}\, = \,\frac{{2 \times 2}}{{5 \times 2}} = \frac{4}{{10}}\, = \,0.4,\frac{7}{8} = \,\frac{{7 \times 125}}{{8 \times 125}}\, = \,\frac{{875}}{{1000}}\, = 0.875\).
3. If the denominator cannot be turned into multiples of \(10\) such as \(11,13,21,27,\) divide the numerator by the denominator to convert the fraction to a decimal value.

Decimal Number System

Decimal Number System is that number system in which a total of ten digits or ‘ten signs’ (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are used for counting/counting. This is the most commonly used number system by humans. For example, 645.7 is a number written in the decimal system.

There are many reasons for the success of this method:

• Use of only ten symbols to represent any number – Ten symbols are neither too many to be remembered nor too few to use symbols too many times to write large numbers.
• For example, to write 255 in the binary number system, eight digits are needed; (255 = 11111111)
• The number ten is very familiar to humans – there are ten fingers in the hands; There are also ten fingers on the feet.

Solved Examples on Decimal Numbers

Q.1. Convert \(\frac{{17}}{{100}}\) into decimals.
Ans: To convert fraction to decimal, divide \(17\) by \(100.\)
Thus, \(\frac{{17}}{{100}}\, = \,0.17\)
Hence, the required decimal form of the given fraction is \(0.17\).

Q.2. Explain \(3.6\) as a decimal number.
Ans: We can read \(3.6\) as,
1. On the left side is \(3\), which is the whole number part.
2. \(6\) is in the tenth position, meaning \(6\) tenths,or \(\frac{6}{{10}}\)
3. So, we can say that \(3.6\) is \(3\) and \(6\) tenths or three-point six.

Q.3. Write the decimal expansion of the number \(4781.52\)
Ans: The decimal expansion of the number can be done by following two steps.
The digits present to the left of the decimal point are multiplied with the positive powers of \(10\) in increasing order from right to left.
The digits present to the right of the decimal point are multiplied with the negative powers of \(10\) in increasing order from left to right.
Hence, the expansion of the number is given below:
\(4781.52 = \left\{ {(4 \times 1000) + (7 \times 100) + (8 \times 10) + (1 \times 1) + (5 \times 0.1) + (2 \times 0.01)} \right\}\)

Q.4. Which is the whole number part and the decimal part in the decimal number \(20.204\)?
Ans: In the given number \(20.204,20\) is the whole number, and \(204\) is the decimal part.

Q.5. How to write \(200.001\) in words?
Ans: \(200.001\) in words can be written as “two hundred point zero one”.

Summary

In this article, we learned about decimal numbers. We also learned about the types of decimal numbers. In addition to it, we learned how we could represent decimal numbers. Finally, we also understood the concept of expanding decimal numbers with the help of an example and converting decimal numbers to fractions and vice versa.

FAQs

Q.1: What are the types of decimals?
Ans: The types of decimal numbers are as follows;
1. Terminating Decimal Numbers
2. Non-Terminating Decimal Numbers
3. Recurring Decimal Numbers
4. Non-Recurring Decimal Numbers

Q.2: Can we say that decimal numbers are integers?
Ans: Fractions and decimals are not integers. Integers can be positive, negative, and zero but cannot be fractions or decimals. Thus, if we take numbers like \(56, – 100,0,\,2021,\) they all come under integers, whereas if we consider numbers like \(\frac{2}{5},\frac{9}{2},5\frac{{13}}{5},3.05,0.001,\,120.120\), they all are not considered as integers.

Q.3: What is \(2.738\) approximated to \(2\) decimal places?
Ans: \(2.738\) can be approximated as \(2.74\) as the digit in the thousandths place is greater than \(5\). So, we have to add one with the digit at hundredths place.

Q.4: What does a decimal point mean?
Ans: A decimal point is a point or dot which is used to separate the whole number part from the fractional part of a decimal number.

Q.5: How do you explain decimal numbers?
Ans: A decimal number is one in which a decimal point separates the whole number and fractional parts.