• Home
• /
• Blog
• /
• What Are Decimals – Definition With Examples

# What Are Decimals – Definition With Examples

July 30, 2022

This post is also available in: हिन्दी (Hindi)

Decimals derived from the word ‘deci’ meaning $10$ are used in our daily life. Be it money,  weight, or length –  the decimals find their place in everyone’s life.  They are used to express the whole number and fraction together. The main goal of the usage of decimal numbers is to acquire more precision.

The decimals use a symbol ‘.’, commonly known as a decimal point to express all types of numbers – whole numbers and fractions. The decimal point separates the whole part from the fractional part of a number.

There are many real-life situations in which you might be using decimals without even realizing it. For example, if a shopkeeper tells you that the price of a pen is $10$ rupees and $50$ paise, then mathematically, it can be represented as ₹$10.50$.

In this article, you’ll learn what are like decimals and unlike decimals and how they are placed in a decimal place value chart.

## What are Decimals?

Decimals are numbers that fall between two whole numbers or integers. For example, $7.5$ is a decimal number lying between $7$ and $8$. It is greater than $7$, and less than $8$ but is not a whole number.

Decimal numbers are the same as fractions but they’re expressed differently.  In the above example, $7.5$ is the same as the mixed fraction $7 \frac {1}{2}$ or the improper fraction $\frac {15}{2}$.

With the help of decimals, you can write more precise values of measurable quantities like length, weight, distance, money, etc. The numbers to the left of the decimal point are the integers or whole numbers and the numbers to the right of the decimal point are decimal fractions.

As you might be knowing that if you move towards the left, the place value of a digit increases 10 times. For example, in $5238$, $8$ is placed at ones, $3$ is placed at tens, $2$ at hundreds, and $5$ at thousands.

Similarly, in the case of digits to the right of the decimal point, the place value of a digit decreases 10 times. For example, in $0.5238$, $5$ is placed at tenths $\left( \frac {1}{10} \right)$, $2$ is placed at hundredths $\left( \frac {1}{100} \right)$, $3$ is is placed at thousandths $\left( \frac {1}{1000} \right)$, and $5$ is placed at tenth-thousandths $\left( \frac {1}{10000} \right)$.

Maths can be really interesting for kids

## Decimal Place Value Chart

As seen above a decimal number consists of two parts

• the whole part: lies to the left of the decimal point
• the decimal part (fractional part): lies to the left of the decimal point

The place values for the whole part are (moving from right to left after the decimal point):

• ones $\left( 1 \right)$
• tens $\left( 10 \right)$
• hundreds $\left( 100 \right)$
• thousands $\left( 1000 \right)$

The place values for the decimal part are (moving from left to right after the decimal point):

• tenths $\left( \frac {1}{10} \right)$
• hundredths $\left(\frac {1}{100} \right)$
• thousandths $\left(\frac {1}{1000} \right)$

Note: There is NOoneths‘ or ‘uniths‘ before a decimal point. Can you guess “Why?“.

### Examples – Decimal Place Value Chart

Let’s consider some examples to understand the decimal place value chart.

Ex 1: $402.874$

Ex 2: $29.905$

Ex 3: $7.04$

Ex 4: $19.003$

Is your child struggling with Maths?
We can help!
Country
• Afghanistan 93
• Albania 355
• Algeria 213
• American Samoa 1-684
• Andorra 376
• Angola 244
• Anguilla 1-264
• Antarctica 672
• Antigua & Barbuda 1-268
• Argentina 54
• Armenia 374
• Aruba 297
• Australia 61
• Austria 43
• Azerbaijan 994
• Bahamas 1-242
• Bahrain 973
• Belarus 375
• Belgium 32
• Belize 501
• Benin 229
• Bermuda 1-441
• Bhutan 975
• Bolivia 591
• Bosnia 387
• Botswana 267
• Bouvet Island 47
• Brazil 55
• British Indian Ocean Territory 246
• British Virgin Islands 1-284
• Brunei 673
• Bulgaria 359
• Burkina Faso 226
• Burundi 257
• Cambodia 855
• Cameroon 237
• Cape Verde 238
• Caribbean Netherlands 599
• Cayman Islands 1-345
• Central African Republic 236
• Chile 56
• China 86
• Christmas Island 61
• Cocos (Keeling) Islands 61
• Colombia 57
• Comoros 269
• Congo - Brazzaville 242
• Congo - Kinshasa 243
• Cook Islands 682
• Costa Rica 506
• Croatia 385
• Cuba 53
• Cyprus 357
• Czech Republic 420
• Denmark 45
• Djibouti 253
• Dominica 1-767
• Egypt 20
• El Salvador 503
• Equatorial Guinea 240
• Eritrea 291
• Estonia 372
• Ethiopia 251
• Falkland Islands 500
• Faroe Islands 298
• Fiji 679
• Finland 358
• France 33
• French Guiana 594
• French Polynesia 689
• French Southern Territories 262
• Gabon 241
• Gambia 220
• Georgia 995
• Germany 49
• Ghana 233
• Gibraltar 350
• Greece 30
• Greenland 299
• Guam 1-671
• Guatemala 502
• Guernsey 44
• Guinea 224
• Guinea-Bissau 245
• Guyana 592
• Haiti 509
• Heard & McDonald Islands 672
• Honduras 504
• Hong Kong 852
• Hungary 36
• Iceland 354
• India 91
• Indonesia 62
• Iran 98
• Iraq 964
• Ireland 353
• Isle of Man 44
• Israel 972
• Italy 39
• Jamaica 1-876
• Japan 81
• Jersey 44
• Jordan 962
• Kazakhstan 7
• Kenya 254
• Kiribati 686
• Kuwait 965
• Kyrgyzstan 996
• Laos 856
• Latvia 371
• Lebanon 961
• Lesotho 266
• Liberia 231
• Libya 218
• Liechtenstein 423
• Lithuania 370
• Luxembourg 352
• Macau 853
• Macedonia 389
• Malawi 265
• Malaysia 60
• Maldives 960
• Mali 223
• Malta 356
• Marshall Islands 692
• Martinique 596
• Mauritania 222
• Mauritius 230
• Mayotte 262
• Mexico 52
• Micronesia 691
• Moldova 373
• Monaco 377
• Mongolia 976
• Montenegro 382
• Montserrat 1-664
• Morocco 212
• Mozambique 258
• Myanmar 95
• Namibia 264
• Nauru 674
• Nepal 977
• Netherlands 31
• New Caledonia 687
• New Zealand 64
• Nicaragua 505
• Niger 227
• Nigeria 234
• Niue 683
• Norfolk Island 672
• North Korea 850
• Northern Mariana Islands 1-670
• Norway 47
• Oman 968
• Pakistan 92
• Palau 680
• Palestine 970
• Panama 507
• Papua New Guinea 675
• Paraguay 595
• Peru 51
• Philippines 63
• Pitcairn Islands 870
• Poland 48
• Portugal 351
• Puerto Rico 1
• Qatar 974
• Romania 40
• Russia 7
• Rwanda 250
• Samoa 685
• San Marino 378
• Saudi Arabia 966
• Senegal 221
• Serbia 381 p
• Seychelles 248
• Sierra Leone 232
• Singapore 65
• Slovakia 421
• Slovenia 386
• Solomon Islands 677
• Somalia 252
• South Africa 27
• South Georgia & South Sandwich Islands 500
• South Korea 82
• South Sudan 211
• Spain 34
• Sri Lanka 94
• Sudan 249
• Suriname 597
• Svalbard & Jan Mayen 47
• Swaziland 268
• Sweden 46
• Switzerland 41
• Syria 963
• Sao Tome and Principe 239
• Taiwan 886
• Tajikistan 992
• Tanzania 255
• Thailand 66
• Timor-Leste 670
• Togo 228
• Tokelau 690
• Tonga 676
• Trinidad & Tobago 1-868
• Tunisia 216
• Turkey 90
• Turkmenistan 993
• Turks & Caicos Islands 1-649
• Tuvalu 688
• U.S. Outlying Islands
• U.S. Virgin Islands 1-340
• UK 44
• US 1
• Uganda 256
• Ukraine 380
• United Arab Emirates 971
• Uruguay 598
• Uzbekistan 998
• Vanuatu 678
• Vatican City 39-06
• Venezuela 58
• Vietnam 84
• Wallis & Futuna 681
• Western Sahara 212
• Yemen 967
• Zambia 260
• Zimbabwe 263
Age Of Your Child
• Less Than 6 Years
• 6 To 10 Years
• 11 To 16 Years
• Greater Than 16 Years

You can read a decimal number in two ways. Let’s consider a decimal number $56.27$.

• In a first way, it is read as eighty-five point two-seven. The whole number is read in the normal way whereas for the decimal part each digit is read separately.
• In a second way, it is read as eighty-five and twenty-seven hundredths. The whole number is read in the normal way and the decimal part is read by its place value in the decimal place value chart.

## Expanded Form of Decimals

You know digits of any whole number can be expanded in terms of their place value. We use a place value chart to write the whole numbers in expanded form.

The number $52864$ can be expanded as $5 \times 10000 + 2 \times 1000 + 8 \times 100 + 6 \times 10 + 4 \times 1$ or $5 \times 10^{4} + 2 \times 10^{3} + 8 \times 10^{2} + 6 \times 10^{1} + 4 \times 10^{0}$

Similarly, digits of a decimal number can be expanded in terms of their place value.

The number $9247.613$ can be expanded as $9 \times 1000 + 2 \times 100 + 4 \times 10 + 7 \times 1 + 6 \times \frac {1}{10} + 1 \times \frac {1}{100} + 3 \times \frac {1}{1000}$ or $9 \times 10^{3} + 2 \times 10^{2} + 4 \times 10^{1} + 7 \times 10^{0} + 6 \times \frac {1}{10^{1}} + 1 \times \frac {1}{10^{2}} + 3 \times \frac {1}{10^{3}}$ or $9 \times 10^{3} + 2 \times 10^{2} + 4 \times 10^{1} + 7 \times 10^{0} + 6 \times 10^{-1} + 1 \times 10^{-2} + 3 \times 10^{-3}$.

## Types of Decimals

Decimals can be divided into different categories depending upon the type of digits occurring after the decimal point. It will depend upon whether the digits are repeating, non-repeating, or terminating. The four types of decimal numbers include

1. Terminating Decimals
2. Non-Terminating Decimals
• Recurring Decimals
• Non-Recurring Decimals

### 1. Terminating Decimals

The number of digits directly after the decimal point in terminating decimal numbers is limited. The number of digits following the decimal point of the ending decimal numbers can be counted so it is finite.

Examples of terminating decimals are $126.543$, $14.7$, $-12.9843$.

All of these decimal numbers are ending decimal numbers or precise decimal numbers because the number of digits following the decimal point is finite.

### 2. Non-Terminating Decimals

Non-terminating decimal numbers are those in which the digits following the decimal point repeat indefinitely. In other words, decimal numbers can have an endless number of digits following the decimal point. Non-terminating decimals are classified as recurring and non-recurring decimal numbers.

#### 2 a. Recurring Decimals

Recurring decimal numbers have an unlimited number of digits following the decimal point. These numerals, however, are repeated at regular intervals.

Examples of recurring decimals are $1.33333…$, $7.21212121…$, $56.123123123…$.

These are examples of recurring decimal numbers, in which the number of digits following the decimal point is repeated at regular intervals or in a predefined order.

These numbers can also be written by placing a bar sign over the number that is repeated after the decimal point. $1.\overline{3}$, $7.\overline{21}$, $56.\overline{123}$.

These numbers can also be represented in fractional form, making them rational numbers.

#### 2 b. Non-Recurring Decimals

Non-recurring decimal numbers are decimals that do not terminate and do not repeat. Non-recurring decimal numbers have an infinite number of digits at their decimal places, and their digits do not follow a fixed order.

Examples of non-recurring decimals: $3.14159265359…$ (value of $\pi$), $32.564321786…$, $-54.73429030281…$

Note: Non-recurring decimal numbers cannot be represented by a bar sign because the digits after the decimal point do not repeat in a predictable order.

## What Are Like Decimals?

Like decimals are the decimal numbers that have the same number of digits after the decimal point. For example, $3.92$ and $5.68$ are like decimals, because both the numbers have $2$ decimal places after the decimal point.

## What Are Unlike Decimals?

Unlike decimals are the decimal numbers that have different number of digits after the decimal point. For example, $6.103$ and $5.23$ are unlike decimals, because $6.103$ has $3$ digits after the decimal point whereas $5.23$ has $2$ digits after the decimal point.

## Conclusion

Decimal numbers are the most commonly used form to represent fractional quantities.  We use these numbers to represent money, weight, capacity, etc. in our day-to-day life. Depending on whether the number of digits after the decimal point is countable or uncountable, the decimals are broadly classified as terminating or non-terminating.

## Practice Problems

1. Write the following numbers in the expanded form
1. $5643.231$
2. $56.095$
3. $92.6750$
4. $729.7865$
5. $2.0008$
2. Write the following numbers in words (Use both the forms)
1. $6754.7865$
2. $87.005$
3. $321.9880$
4. $78.00008$
5. $309.40405$