A Complete Guide On Decimal Fractions by Experts

Everything To Know About Decimal Fractions: Elaborative Fundamentals+ Examples

Mathematics is not about numbers, equations, computations, or algorithms; it is about understanding

-William Paul Thurston

Have you ever found yourself stuck in gridlock while solving a mathematics problem as you couldn't comprehend the steps to reach an accurate conclusion? You know, it's right there, dangling on the edge of your memory, but simply out of reach enough for you not to remember it instantly.

Since our childhood, we have hammered that math is a daunting subject with innumerable tricky and complicated formulas. The complex calculations and formulae involved frighten countless students to the core. One such complicated problem is converting a decimal to a fraction.

Decimal fractions are one of the most frequently carried out steps in mathematics. However, to do so accurately, it is essential to have the concepts of your division basics in place. Once you get the hang of these fundamentals, you can easily find answers to the addition or subtraction of decimal fractions.

To aid you in today's comprehensive post, we will walk you through certain remarkable ways and guidelines that can be your best buddy next time when you're faced with a tricky problem of finding the place value of decimal fractions and don’t have a calculator handy.

Let’s dive right in!

Introduction of Decimal A Fraction

The prerequisites for comprehending decimal fractions are gaining a profound knowledge of normal functions. One must know the fraction comprises a numerator and a denominator. The proper way of writing a fraction is-

X/y

X is the numerator in this example, and y is the denominator. Decimal fractions are the fractions in which the denominator (y in this example) must be 10 or a multiple of 10 like 100, 1000, 10000, etc. The numerator can be any integer (between –infinity and +infinity). These decimal fractions are generally expressed in decimal numbers (numbers with a decimal point).

Examples-

7/10000 is a decimal fraction. It is presented in the decimal form as 0.0007.

Types Of Decimal A Fraction

Decimals can be classified into the following types based on their decimal places-

Non-Recurring or Terminating Decimal- As the name implies, non-recurring means that do not reoccur or repeat, i.e., they terminate or end like 0.5, 0.10, 0.25, and 0.125. To convert these fractions, the numerator is divided by the denominator. If you need to convert ¼ into a decimal, divide 1 by 4 to get the answer 0.25.

Recurring or Non-Terminating Decimal- Recurring means they do not terminate or come to an end. To convert these fractions, divide the numerator by the denominator. Like, if you need to convert 1/3 into a decimal, divide 1 by 3 to get the answer as 0.333

Numerator and Denominator of Fractions

The numerator and denominator are parts of fractions separated by a horizontal bar, popularly known as vinculum. The numerator indicates the upper part of the fraction, and the denominator is the lower part of the fraction. When we represent the numerator and denominator, we treat the numerator as the dividend and the denominator as the divisor.

Like, 4/5 is a fraction. Here 4 is the numerator, and 5 is the denominator.

Place Value of Decimal Fractions

A decimal number comprises a whole number, and a fractional part separated by the dot is called the decimal point.

The decimal fraction place value chart demonstrates the place value of digits in a decimal number. The first digit after the decimal fraction represents the tenth place. The next digit after the decimal fraction represents the hundredth place.

If we observe the chart given above, you will see the place values before the decimal start with ones, followed by tens, hundreds, etc. While the place value after the decimal point starts from tenths, followed by hundredths, then thousandths, and so on. The number 0.26 is made up of 2 tenths and 6 hundredths. This can also be presented as 0.26= 0.2+ 0.06. In other words, it implies 0.26= 2/10 + 6 /100.

Operations on Decimal Fractions

As we all know, there are four basic operations in Mathematics- addition, subtraction, multiplication, and division.

Let’s dive deep to understand the different operations performed on decimal fractions-

Addition of Decimal Fractions

By now, we hope it is clear to you that decimal fractions have 10,100, 1000 and so on as their denominators. To add two or more decimal fractions, you can implement the ways enlisted below-

By converting the decimal fractions to decimals and then adding.
By converting the given decimal fractions to like fractions and then add.

If you want to implement the first method, you will want to first convert decimal fractions to decimals and then add those values. Like, let us add 2/10 +34/100.

2/10 can be written as 0.2, and 34/100 can be written as 0.34. So, 0.2+0.34= 0.54.

So, 2/10 +34/100= 0.54, which can be written as 54/100.

Now, you can also add the same numbers using the second method. To convert the given fractions (2/10 and 34/100) into like fractions, we will find the LCM of the denominators. The least common multiple of 10 and 100 is 100. Thus, multiply the numerator and denominator of 2/10 by 10.

2/10= (2*10)/ (10*10)
2/10= 20/100

Now, 20/100 +34/100= 54/100. Therefore, 2/10 +34/100=54/100.

Subtraction of Decimal Fractions

The subtraction of decimal fractions is done the same way as an addition. For instance, 44/100 -1/10 can be calculated as 0.44-0.1, equals 0.34 or 34/100.

Another way to subtract 1/10 from 44/100 is to find the LCM of the denominators and convert them into like fractions. The LCM of 100 and 10 is 100. Thus, multiply the numerator and denominator of 1/10 by 10.

1/10= (1*10)/ (10*10)
1/10= 10/100

Now, 44/100- 10/100= 34/100. Thus, 44/100- 1/10=34/100.

Multiplications of Decimal Fractions

The multiplications of decimal fractions are evaluated by multiplying the numerators and denominators separately. To multiply the power of 10, you need to simply add the numbers of zeroes.

Like, 7/10 *3/100 = (7*3)/(10*100)= 21/1000.

Division of Decimal Fractions

You can implement the below-enlisted steps to divide two decimal fractions-

Step 1- Find the reciprocal of the second fraction
Step 2- Multiply the first fraction with the reciprocal of the second fraction

It is the same as a normal division of fractions. Like, 25/10/ 5/100= 25/10 *100/5. This means 5*10= 50. Hence, 25/10/ 5/100= 50.

Examples of Decimal Fractions

Example 1- A tank has 56.32 litres capacity. If Martha used 21.19 litres, how much water is left in the water tank?

Solution-

Capacity of the tank= 56.32 litres

Amount of water used = 21.19 litres

Amount of water left in the tank= 56.32- 21.19= 35.13 litres.

Example 2- Samantha bought 12 bags of wheat flour, each weighing 4563/100 kilograms. What will be the total weight?

Solution-

Total number of bags= 12

Weight of each bag= 4563/100 kg= 45.63 kg

Total weight= 45.63*12= 547.66kg.

Example 3- If the product of 38.46 and another number is 658.17, what is the other number?

Solution-

One number= 38.46

Product of two numbers= 658.17

The other number= 658.17/ 38.46

= 658.17/100 / 38.46/100

= 17.11

Mastering essential concepts like a decimal fraction in the early years is the key to success in the classroom. Save this post on the laptop. Take the help of this comprehensive guide and form an in-depth understanding of decimal fractions to not only become a confident problem solver in life. Here's wishing all the luck!

Frequently Asked Question by Students

Q.1.How to convert a fraction to a decimal?

ANS.Use the method of long division to convert a fraction to a decimal. You can also use another method like finding a number you can multiply by the bottom of the fraction to make it 10,100, or 1000 or any 1 followed by 0s. Then, multiply the top and bottom by that number. After that, write down just the top number to put the decimal in the correct spot.

Q.2.How to turn a fraction into a division problem?

ANS.Dividing numbers is easy with a calculator. If you need to do long division by hand, put the numerator inside the division bracket and the denominator outside, to the left of the division bracket.

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