Decimals were invented by the Chinese at the end of the 4th century BC, and they quickly spread throughout the Middle East and Europe. Decimals come in handy in everyday life when dealing with money, weight, and length. When we need a more precise value for something, decimals are required. Humankind has been Using Decimals for a very long time now.

Decimals are a shorthand way of writing fractions and mixed numbers with denominators of powers of ten, such as 10,100,1000,10000, and so on. If a number has a decimal point, the number of tenths is shown by the first digit to the right of the decimal point.

Scientists and engineers use decimals for the majority of their computations. Real-life examples make it easier to grasp the concept of decimals. This article discusses the concept of decimal application in everyday life.

Decimals Definition

In algebra, a decimal point is used to separate the whole number part, and a fractional part such a number is known as a decimal number. The dot or point in a decimal number is called a decimal point. The digits after the decimal point indicate a value less than one. 

Decimals are based on the preceding powers of \(10\). Thus, as we proceed from left to right, the place value of digits gets ten times smaller, meaning the decimal place value will be the tenths, hundredths, and thousandths. A tenth means one-tenth or \(\frac{1}{{10}}\). One-tenth in decimal form is \(0.1\). Hundredth means \(\frac{1}{{100}}\). One-hundredth in decimal form is \(0.01\) and so on.

Example:

\(1.25,\,0.965,\,100.0004,\,0.0000075,\,8.3333\) etc are some examples of decimals.
The following figure shows the decimal number with the place value of each digit.

How Long Can a Decimal be?

A decimal number can have any number of decimals after the point, in the case of the numerical value of \({\rm{Pi}}\). Below we have abbreviated it to \(50\) decimal digits.

\({\rm{Pi}} = 3.14159\,26535\,89793\,23846\,26433\,83279\,50288\,41971\,69399\,37510 \ldots .\)

Decimal Digits

Consider a decimal number \(1.0874\). After the point, the digits \(0,\,8,\,7\) and \(4\) are the decimal digits. In this way, the digits after the point are known as the decimal digits.

Decimal Expansion and Representation

The tenth is the division of one unit into ten equal parts. The hundredth is the division of one unit into \(100\) equal parts, and the thousandth is the division of one unit into \(1000\) equal parts. These can be represented on a number line. The number line below shows the decimal number with a tenth as \(1\) unit is equally divided into \(10\) divisions.

Write Each Phrase as Both Fraction and Decimal Number

Phrase	Fraction	Number
three tenths	\(\frac{3}{{10}}\)	\(0.3\)
seven hundredths	\(\frac{7}{{100}}\)	\(0.07\)
thirty-nine hundredths	\(\frac{{39}}{{100}}\)	\(0.39\)
three hundred fifty-three thousandths	\(\frac{{353}}{{1000}}\)	\(0.353\)

Uses of Decimals in Daily Life

Decimals are needed in situations where we need the precise value of something than the rounded-off value. For instance, when we check our height in feet, we have to be precise at \(5.4\) feet. We cannot round off to\(5\) or \(6\) feet, as that small measurement is what matters. We use decimals in three important fields in our daily life- while managing money, weighing the weight, and measuring the length. Let us discuss with examples.

Use of Decimal to Represent Money

When you are dealing with money, you cannot escape from decimal numbers. We, at some point, need to calculate the cash in terms of paisa. Assume yourself buying half a \({\rm{kg}}\) of sugar. You go to the neighbouring shop and learn that the cost of \(1\;{\rm{kg}}\) sugar is \(₹53\). What is the amount you are going to give to the shopkeeper? You need to divide \(53\) by \(2\) to find the cost of half a \({\rm{kg}}\) of sugar. So you find that the cost of half \({\rm{kg}}\) sugar is \(₹26.50\).

Thus, the decimal concept emerges. To hand over the amount, we must understand what \(26.5\) means in terms of rupees. Let us recall the relationship between the rupee and the paisa

\(₹1 = 100\) paise
\(₹0.5 = 50\) paise
\(₹26.5 = ₹26\) and \(50\) paise

Thus, you need to give the shopkeeper \(26\) rupees and \(50\) paise to buy half a \({\rm{kg}}\) of sugar.

Interconverting, we have \(1\) paisa \( = ₹\frac{1}{{100}} = 0.01\) 

Let us consider a basic example to become familiar with decimals.

Example 1: Convert \(185\) paise to ₹.

As we know, \(1\) paisa \( = ₹\frac{1}{{100}}\)

So, \(185\) paise \( = ₹\frac{{185}}{{100}} = ₹1.85\)

Example 2: Convert \(350\) paise to the rupee.

As we know, \(1\) paisa \( = ₹\frac{1}{{100}}\)

So, \(350\) paise \( = ₹\frac{{350}}{{100}} = ₹3.50 = ₹3\) and \(50\) paise.

Use of Decimal to Represent the Length

When you measure the length of something, it is uncertain that it is multiple of given graduation. For example, you want to measure the distance between two cities. You may say the approximate distance is \(350\;{\rm{km}}\), but in actuality it may not be exactly \(350\). It may be \(350\;{\rm{km}}\) and \(500\;{\rm{m}}\). In conditions like this, decimals are useful-some of the useful relationships of units related to the length.

\(1\;{\rm{km}} = 1000\;{\rm{m}}\)
\(1\;{\rm{m}} = 100\;{\rm{cm}}\)
\(1\;{\rm{cm}} = 10\;{\rm{mm}}\)

Presently, the distance between two cities is

\(348\;{\rm{km}} + 500\;{\rm{m}} = 348\;{\rm{km}} + \frac{{500}}{{100}}\;{\rm{km}} = (348 + 0.5){\rm{km}} = 348.5\;{\rm{km}}\)

Let us look into few examples:

Example 1: Converting \(348.5\;{\rm{cm}}\) into meters. As we know, \(100\;{\rm{cm}} = 1\;{\rm{m}}\)

Or \({\rm{cm}} = \frac{1}{{100}}{\rm{m}}\)

\(348\;{\rm{cm}} = 348 \times \frac{1}{{100}}{\rm{m}} = \frac{{348}}{{100}}{\rm{m}} = 3.48\;{\rm{m}}\)

Example 2: Converting \(61\;{\rm{km}}\) and \(25\;{\rm{m}}\) into decimal.

As we know, \(1\;{\rm{km}} = 1000\;{\rm{m}}\)
So, \(1\;{\rm{m}} = \frac{1}{{1000}}\;{\rm{km}}\)
\(61\;{\rm{km}} + 25\;{\rm{m}} = 61 + \left( {25 \times \frac{1}{{{\rm{roo}}0}}} \right){\rm{km}} = 61.025\;{\rm{km}}\)

Use of Decimal to Represent the Weight

Here is another sector where the decimals become necessary, i.e., while managing the weight. For example, if you want to buy any fruit, rarely will the weight be an entire number. Consider buying a muskmelon; we know that the weight of a muskmelon will be more or less \(2\;{\rm{kg}}\).

In such a case, the seller has to calculate the amount to be charged in terms of its weight. As we know, the relation between \({\rm{kg}},\,{\rm{gm}}\) and \({\rm{mg}}\).

\(1\;{\rm{kg}} = 1000{\rm{gm}}\)
\(1\;{\rm{gm}} = 1000{\rm{mg}}\)

Currently, assuming the weight of one muskmelon is \(1\;{\rm{kg}}\) and \(250\,{\rm{gm}}\). In this case, the shopkeeper has to charge for that \(250\,{\rm{gms}}\) extra too. So the total weight of muskmelon \( = 1\;{\rm{kg}} + 250{\rm{gm}} = 1\;{\rm{kg}} + \frac{{250}}{{1000}}\;{\rm{kg}} = 1\;{\rm{kg}} + 0.25\;{\rm{kg}} = 1.25\;{\rm{kg}}\)

Example 1: Convert \(250\,{\rm{gm}}\) to \({\rm{kg}}\)

We know that, \(1000\,{\rm{gm}} = 1\;{\rm{kg}}\)
Or, \(1\,{\rm{gm}} = \frac{1}{{1000}}\;{\rm{kg}}\)
\(250.9\,{\rm{m}} = 250 \times \frac{1}{{1000}}{\rm{kg}} = \frac{{250}}{{1000}}\;{\rm{kg}} = 0.250\;{\rm{kg}}\)

Example 2: Represent \(5\;{\rm{kg}}\) and \(396\,{\rm{gm}}\) in decimal.

As we know, \(1\,{\rm{gm}} = \frac{1}{{1000}}{\rm{kg}}\)
\(396\,{\rm{gm}} = \frac{{396}}{{1000}}\;{\rm{kg}}\)
So, \(5\;{\rm{kg}} + 0.396\;{\rm{kg}} = 5.396\;{\rm{kg}}\)

Solved Examples – Using Decimals

Q.1. The weight of a bag of sugar is \(50760\;{\rm{g}}\). What will be the weight in \({\rm{kg}}\)?
Ans: Given, \(50760\;{\rm{g}}\)
We know that \(1\,{\rm{gm}} = \frac{1}{{1000}}\;{\rm{kg}}\)
\(50760\,{\rm{gm}} = \frac{{50760}}{{{\rm{ rooo }}}}{\rm{kg}} = 50.76\;{\rm{kg}}\)
Thus, the weight of the bag of sugar is \(50.76\;{\rm{kg}}.\)

Q.2. The length of a bed is \(3\,{\rm{m}}\) and \(25\,{\rm{cm}}\) Write the length of the bed in meters.
Ans: Given the length of a bed is \(3\,{\rm{m}}\) and \(25\,{\rm{cm}}\)
We know that \(1\;{\rm{m}} = 100\;{\rm{cm}}\) or \(1\;{\rm{cm}} = \frac{1}{{100}}\;{\rm{m}}\)
\(3\,{\rm{m}}\) and \(25\;{\rm{cm}} = 3\;{\rm{m}} + \frac{{25}}{{400}}\;{\rm{m}} = 3\;{\rm{m}} + 0.25\;{\rm{m}} = 3.25\;{\rm{m}}.\)
Thus, the length of the bed is \(3.25\,{\rm{m}}.\)

Q.3. Convert \(78\,{\rm{cm}}\) to \({\rm{km}}\)
Ans: As we know, \(1\;{\rm{km}} = 1000\;{\rm{m}}\) and \(1\;{\rm{m}} = 100\;{\rm{cm}}\)
So \(1\;{\rm{km}} = 1000 \times 100\;{\rm{cm}} = 100000\;{\rm{cm}}\)
\(1\;{\rm{cm}} = \frac{1}{{100000}}\;{\rm{km}}\)
\(78\;{\rm{cm}} = 78 \times \frac{1}{{100000}}\;{\rm{km}}\)
\( \Rightarrow 78\;{\rm{cm}} = 0.00078\;{\rm{km}}.\)

Q.4. Convert \(₹35\) and \(70\) paise to decimal.
Ans: As we know, \(1\) paisa \( = ₹\frac{1}{{100}}\)
So, \(70\) paise \( = ₹70 \times \frac{1}{{100}}\)
\(₹35 + ₹\frac{{70}}{{100}} = ₹35.70.\)
Thus, \(₹35\) and \(70\) paise converted to decimal is \( = ₹35.70.\)

Q.5. The total cloth required to stitch \(10\) shirts is \(32\,{\rm{m}}\). How much cloth is required for stitching one shirt?
Ans: Given, length of cloth for \(10\) shirts \( = 32\,{\rm{m}}\)
Length of cloth for \(1\) shirt \( = \frac{{32}}{{\rm{m}}} = 3.2\;{\rm{m}}\)
Thus, \(32\,{\rm{m}}\) of cloth is required for stitching one shirt.

Summary

This article is about the uses of decimals. Here we understand the decimal numbers, how they are written and read. Also, how they are expanded with examples. Then we discussed the importance of decimals. There comes a need to learn decimal numbers. Further, we have learnt the main fields (money, length, and weight) where decimals play a very important role. A good number of examples have been solved to make the concept clear for students.

Frequently Asked Questions

We have provided some frequently asked questions on Using Decimals here:

Q.1. How many types of decimals are there?
Ans: Decimals are three types; they are
1. Terminating decimal
2. Non-terminating but recurring decimal
3. Non-terminating and non-recurring decimal

Q.2. What are some everyday life examples of decimals?
Ans: Some of the everyday life examples of decimals are used while handling weight, money, length, etc. We use decimals when we need a more precise measurement of something. For example, if we want to buy half \({\rm{kg}}\) of daal, the shopkeeper weights precisely \(0.5\;{\rm{kg}}\) and packs it.

Q.3. What is the importance of decimals?
Ans: People use decimals in everyday life in different circumstances such as price tags, measuring height, reading Olympic scores, etc. Decimals are the way of expressing large and small numbers by using a decimal point.

Q.4. What is a decimal?
Ans: Decimals are another way of expressing the fractions and mixed fractions with denominators multiples of \(10\) like \(10,\,100,\,100,\,1000\) etc. The decimal number has the whole part and the decimal part. The first number on the right side of the decimal indicates the number of the tenth.
For example, \(0.4\) is the same as the fraction \(\frac{2}{5}.\)

Q.5. What is a decimal example?
Ans: Examples of decimals are \(0.25,\,0.667,\,12.678,\,1.625\).

Now you are provided with all the necessary information on the various usage of decimals and we hope this detailed article is helpful to you. If you have any queries regarding this article, please ping us through the comment section below and we will get back to you as soon as possible.