Decimal Numbers
What is a Decimal?
The word decimal is derived from the Latin word Decimus, which means tenth, and the number 10 (or decem).
A group of numbers that are positioned between integers on a number line are known as decimal. Whole numbers, usually referred to as integers, are shown to the left of the decimal point, while decimal fractions are shown to the right of the decimal point.
Decimals allow us to express measurable quantities like length, weight, distance, money, etc. with greater accuracy.
An example of a decimal number is 22.3.
In this case, the whole number part is 22, and the fractional part is 3.
What is the Difference Between a Decimal and a Fraction?
There are only two methods to express numbers: fractions and decimals. While decimals connect the whole integer and fractional parts with a decimal point, fractions are expressed as p/q, where q does not equal 0.
Let’s understand this with the help of an example:
There is one complete cake and one-half of another cake in the image.
Two approaches can be used to illustrate this:
We can express that there is one and a half of a cake in fractional form. That equals one and a half cakes.
Another approach can be expressed as 1.5 cakes in decimal form. In this case, the dot stands in for the decimal point, the number before the dot, in this case, “1,” stands for one complete cake, and the number after the decimal point, or the fractional component, is represented by the half of the cake.
How to Read a Decimal Point?
The popular way to read a decimal is to first read the whole number as you would any whole number, then the decimal point as “point,” and finally each individual digit of the rational part.
For instance, the number is 62.51. So we are going to read the number as sixty two point five one.
What are the Different Types of Decimals?
1. Non-Recurring or Terminating
As the name implies, non-recurring numbers are those that come to an end or don’t recur, such as 0.5, 0.25, and 0.125. These fractions are converted by dividing the numerator by the denominator alone. Divide 1 by 4 to obtain the decimal equivalent of 1/4, for instance, which is 0.25.
2. Recurring or Non-terminating Decimal
As the name implies, repeating indicates that anything happens again and again; it never ends. For example, 0.333…, 0.545454…, etc.
3. Pure Recurring Decimal
They are those decimals in which every digit or group of digits (after the decimal point) repeats. e.g. 0.7777…or 2.373737….. .
4. Mixed Recurring Decimal
This sort of repeating decimal has a set of digits or a group of digits that repeat after the decimal point but one or more of the digits do not. e.g. 1.4232323…
How to Add & Subtract Decimals?
The same rules that apply to adding and subtracting whole numbers also apply to decimals.
1. First convert decimals to like decimals.
Decimals are those that have the same number of digits following the decimal point.
We can add zeros to the extreme right digits in the decimal component of a number to make decimals by doing so because it has no effect on the value.
For instance, 5.2 is equivalent to 5.20, which is equivalent to 5.200.
Let’s take the other number as 2.03.
2. Second, in order of the digits’ locations, write the decimals one below the other.
3. Third, add or subtract the digits working your way leftward from the rightmost digit.
How to Multiply Decimal Numbers?
Steps to Multiply a Decimal
1. First, multiply the values as you would normally do, disregarding the decimal point.
Let’s say the numbers are 5.20 and 2.3.
2. Next, the decimal point must then be added to the solution.
5.20 = 2 numbers after the decimal
2.3 = 1 number after the decimal
Total = 3 numbers after the decimal
11.960 = Answer
How to Divide Decimal Numbers?
Steps to Divide a Decimal:
- The decimal number’s whole number component must be divided by the divisor.
- Put the quotient’s decimal point above the dividend’s decimal point before bringing the tenth digit down.
- Write 0 in the quotient and in front of the tenth digit if the obtained dividend’s tenth digit cannot be divided by the divisor. If not, continue with the division process.
- Repeat the previous step as necessary, adding zeros to the dividend each time, until the remainder has the value 0.
How to Order Decimal Numbers?
Decimal ordering can be challenging. Because when we compare 0.82 and 0.802, we frequently assume that 0.802 is larger because it has more digits, but no it’s not the answer.
Steps to determine which decimals are larger
- Create a table and position the decimal point in the same location for all of the numbers.
- Enter each digit.
- Put zeros in the empty spaces.
- Using the first column on the left, compare.
- Move on to the next column to the right if the digits are equal, continuing until one number wins.
This shows that 0.82 is a larger number.
How to Convert from a Fraction to a Decimal?
To convert any decimal from any fraction, follow the following steps:
1. First write the fraction, and simply divide the numerator by the denominator.
2. Even if the number is not getting divided fully, use the power of decimal to add zeros to the numerator.
For example- 19/3
How to Convert from a Decimal to a Fraction?
To convert any decimal from any fraction follow the following steps
1. First write the decimal split by 1 as shown= Decimal/1
2. Second, for every integer following the decimal point, double the top and bottom values by 10.
For instance, use 100 if there are just two digits after the decimal point, 1000 if there are three, etc.
3. Now make the fraction simpler (or smaller).
For instance, since the number eight is in the tenth place in the fraction 0.8, we multiply it by 10 and get the comparable fraction 8/10.
Quiz
0.92307692307
Quiz
The 3 types of decimals are:
- Non-Recurring or Terminating
- Recurring or Non-terminating Decimal
- Pure Recurring Decimal
Yes, exact decimal numbers are another name for these kinds of decimal numbers. The number of digits following the decimal point in these decimal values is finite.
To convert 400% into a decimal:
400/100 = 4
So the decimal form can be written as 4.0.
This means you have to round off this number for the hundredth place.
2.738
Compare the digit 8 to 5.
Whether it is <, > than 5.
If the digit is less than 5, you convert the right side of the digit to zero.
If the digit is more than 5, you increase the digit by 1 and convert the right side of the digit to zero.
In case of 2.738
The digit 8 is more than 5 therefore, we will increase the digit by 1, and thus 2.74 will be the answer.
First let’s convert 9/15 into decimal which is = 0.6
There is no other digit after .6, ans 9 is wholly divided by 15 after the decimal, thus
9/15 a terminating decimal.
Conclusion
We frequently use decimals while managing money, weight, length, and other variables. When greater precision is needed than whole numbers can provide, decimal numbers are used. For instance, determining the size of a cyst inside a person’s body or the size of an eye cataract that has developed.
For children, it’s highly imperative that they have a solid foundation in mathematics, whether it is fractions or decimals. {igebra.ai} offers online classes for mathematics for students studying in grades 1 to grade 8. Math class comprises various math worksheets, ncert math solutions, and math puzzles for kids to make the learning more interesting.
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