A decimal number system is used to express the whole number and fraction together. Here, we will separate the whole number from the fraction by inserting a ".", which is called a decimal point. For example, let's say you are going to take a cone of ice cream. The vendor tells you that the price of ice cream is $2 and 50 cents. Now, if you want to express this whole amount in one figure, you will say that the price of the ice cream cone is $2.50. There are many such real-life situations in which you might be using decimals without even realizing it. Let us understand the concepts of decimals in a clear way with the help of this article.
|1.||What are Decimals?|
|3.||Rounding Decimals to the Nearest Tenth|
|5.||Types of Decimals|
|6.||FAQs on Decimals|
What are Decimals?
Decimals are a set of numbers written together with a dot in between them that is called a decimal point. 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 called decimal numbers. If we go right from the ones' place, the next place will be (1/10) times smaller, which will be (1/10)th or one-tenth position.
In the case of decimals, for the whole number part, the place value system is the same as the whole number. But after the decimal point, there is a different world of numbers going on in which we use decimal fractions to represent the value. When we are going towards the left, each place is ten times greater than the previous place digit. So, to the right of one's place, we have tenths (1/10) and to the right of tenths, we have hundredths (1/100), and so on. Let us look at some examples for more clarity.
Reading Decimal Numbers: There are two ways to read a decimal number. The first way is to simply read the whole number followed by "point", then to read the digits in the fractional part separately. It is a more casual way to read decimals. For example, we read 34.56 as thirty-four point fifty-six. The second way is to read the whole number part followed by "and", then to read the fractional part in the same way as we read whole numbers but followed by the place value of the last digit. For example, we read 34.56 as thirty-four and fifty-six hundredths.
Let us understand this with an example. We have to write the number 123.456 as words. The above decimal number can be written in words as, One hundred twenty-three and four-hundredth fifty-six thousandth, or one hundred twenty-three point four five six. For example, let us try to find out how the decimal number 85.64 can be written in words.
Rounding Decimals to the Nearest Tenth
Rounding a decimal number or rounding decimals is done by taking the digit in the hundredth place into consideration. The digit in this hundredth's place can have two variations. First, if that number is 4 or less, just remove all the digits to the right of the tenth's digit and the remaining portion is our desired result. But if that number is 5 or greater, we need to increase the tenth place's digit by 1, and then remove all the digits on the right of the tenths digit.
For example, let us try rounding 765.27446 to the tenths place. As we can see, the hundredth place digit in 765.27446 is 7. Now, since 7>5, therefore, to round this number to the nearest tenth place, we add one to the tenth place digit and delete the rest. Hence, when we round off 765.27446 to the nearest tenths place, the result will be 765.3.
In order to compare the decimals, keep the following two things in mind. First, compare the digits before the decimal point, if they are less than or greater than the other number, then it is greater than or less than respectively the other number. Second, if the digits before the decimal point are equal to each other then we compare the first digit after the decimal point which is the tenth digit, and examine which is greater or smaller. We repeat this process and keep on comparing digits to the right until we get the unequal digits.
For example, let's compare 23.789 with 23.759. Here we see digits before the decimal point are equal which is 23 = 23. Now moving on to the tenths digits to compare. i.e., 23.789 with 23.759, we get 7 = 7. Both of them are equal. Now we move to the next term to the right of the tenths digit which is the hundredth digit. i.e., 23.789 with 23.759. Now, since 8>5, then we can say that 23.789 > 23.759. ∴ 23.789 > 23.759.
Types of Decimals
Decimals can be divided into different categories depending upon what type of digits occur after the decimal point. It will depend upon whether the digits are repeating, non-repeating, end, or un-ending (infinite digits after the decimal point). Let us have a look at how the decimals are categorized based on their type here.
- Terminating decimals: Terminating decimals mean it does not reoccur and end after a finite number of decimal places. For example: 543.534234, 27.2, etc.
- Non-terminating decimals: It means that the decimal numbers have infinite digits after the decimal point. For example, 54543.23774632439473747..., 827.79734394723... etc. The Non-Terminating decimal numbers can be further be divided into 2 parts:
- Recurring decimal numbers: In Recurring Decimal Numbers, digits repeat after a fixed interval. For example, 94346.374374374..., 573.636363... etc,
- Non- recurring decimal numbers: Non- Recurring Decimal Numbers, digit never repeat after a fixed interval. For example 743.872367346.., 7043927.78687564... and so on.
Interesting Facts and Notes on Decimals
Below given are some interesting facts and notes on the topic of decimals. This will help you in understanding the topic faster.
- Fact: The number system most commonly used today is based on the Hindu-Arabic number system, which was developed in what is now India around 300 B.C.
- Fact: The prefix "deci" in the word "decimal" means ten.
- Note: Always remember to add the decimal point after the one's place so that we know from where the fraction begins.
Solved Examples on Decimals
Solved Examples on Decimals
Example 1: Raven bought 100 apples from a nearby fruit vendor but later found out that 5 of them were rotten. Can you tell the fraction as well as decimals of the rotten apples to the total apples bought by Raven?
Here, we have 5 rotten apples out of 100. So our fraction becomes, (5/100) or 1/20. Now, how do we write it as decimals? Such problems are solved by dividing the numerator by the denominator. Here, we need to divide 5 by 100. To divide 5 by 100, we will simply shift it by 2 decimal places on the right. The number of decimal places we can shift in the numerator depends upon the trailing zeroes the whole number in the denominator has. Thus, after division, we get: 5/100 = 0.05. Therefore, rotten apples to the fresh apples in the fraction is 0.05.
Example 2: A gas station sold 665.45745 gallons of gas in a day. How many gallons of gas did the gas station sell when rounded to the nearest tenths of the decimal place?
Here, total gallons of gas sold by a gas station in a day = 665.45745. Now, we know that in order to round off to the nearest tenth, we check the digit at the hundredth place, i.e. 55 in 665.45745. Now, since 5 ≥ 5, hence, we add 1 to the digit at the tenths place and drop all the digits on its right side. So gallons of the gas did the gas station sell rounded to the nearest tenths of the decimal place is 665.5 gallons.
Practice Questions on Decimals
Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.
FAQs on Decimals
What is a Non-Decimal Number?
All the natural numbers without any fractional part are non-decimal numbers. For representing these we do not use a decimal point. Also, there is no tenth place or hundredth place in these numbers. For example, 34, 5637, 8765 etc.
How to Read Decimals?
Read the whole number part followed by "and", then read the fractional part in the same way as we read whole numbers but followed by the place value of the last digit. The decimal number is always read as individual digits. As an example, we would read a decimal number of 145.367 as one hundred and forty-five point three six seven.
Are Decimals Integers?
Every Integer can be represented in the form of Decimals, for example, 12.00. But decimals are not integers as integers are not in the form of p/q. By default, an integer can be considered as a decimal. For performing arithmetic operations involving integers and decimals, the integers are to be converted as fractions. For the addition of 4 to 3.36, we convert the 4 as 4.00.
Why do We Use Decimals?
Decimals are used to make our calculations easy. We use them to quickly compare fractions without doing many calculations. For example, comparing (675/63) with (463/77) can be very time-consuming, instead, we write them as decimals 10.71 to 6.01 and compare easily and determine which one is greater than the other. We also use them to shorten the complicated fractional equations. We use decimals every day while dealing with money, weight, length, etc. Decimal numbers are also used in situations where more precision is required which whole numbers cannot provide.
How to Round Decimals?
To round a decimal number look at the next digit to the right side of the place up to which we want to round off. If the digit is less than 5, round down to the previous number and if the digit is 5 or more than 5, round up to the next higher number. The decimal 3.284 can be rounded to 3.28, and the decimal of 4.68 is rounder
What are Repeating and Non-Repeating Decimals?
Repeating Decimals are those in which one or more digits repeat again and again, for example, 1/3 = 0.3333333, while non-repeating decimals are those that end after a specific number of digits, for example, 1/2= 0.5. Another example of a non-rounding decimal is 22/7 = 3.142857.
How do you Write in Decimals?
Decimals are used to express the whole number and fraction in a single notation. In decimals, whole numbers and fractions are separated by a point known as a decimal point. For example, In 65.4, 65 is a whole number and 4 is the fractional part (4/10).
What is 1/4 in Decimals?
Let us see how to represent 1/4 in decimals. Here multiply the numerator and the denominator with a 25, to obtain a 100 in the denominator. Further, we need to convert this fraction with a denominator of 100, as a decimal.
1/4 x 25/25 = 25/100 = 0.25