A Set Of Decimal Fractions

Decimal fractions Math is the representation of the decimal form of fractions, whose denominator is ten or college powers of 10, similar 100, 1000, 10000, etc. For example 1/x, ane/100, one/1000, are fractions in decimal. If we simplify such fractions, we tin write them in the decimal class such equally 0.1, 0.01, 0.001, etc. It is piece of cake to solve mathematical problems that are represented in the class of decimal fractions, such as dividing fractions, multiplying fractions, etc.

A fraction represents a role of the whole. For instance, it tells how many slices of a pizza left or eaten with respect to the whole pizza-like, 1-one-half, iii-quarters. Generally, a fraction has ii parts i.due east. the numerator and the denominator. A decimal fraction is a fraction where its denominator is a ability of 10 i.e. ten¹,x², 10³ etc.

What are Decimal Fractions?

The fractions in which the denominator is equal to 10 or multiples of x (such as 100, yard, grand, 10000, etc.), are known as decimal fractions.

Examples:

i/10 = 0.1
2/100 = 0.02
7/1000 = 0.007

Numerator and Denominator of Fractions

As we already know, fractions are the parts of something whole. It is represented equally a/b, where a and b are the integers. The integer above the bar is the numerator and below the bar is the denominator.

The numerator states the number that is equal parts and denominator states the number of parts of a given number. Let us meet here some of the atmospheric condition for fractions:

If numerator and denominator have equal values and then the fraction is 1.
If numerator is equal to 0, so the fraction is 0.
If denominator is equal to 0, then the fraction goes to infinity.
A decimal fraction is known as a recurring decimal when the digit after the decimal keeps on repeating.

Place Value of Decimal Fractions

We know for the whole number, the place value of digits starts from ones, tens, hundreds, thousands, ten-thousands and and so on, moving from right to left.

In the case of decimal fractions, since we are considering here the decimal point, thus the place value of digits are taken into account from left to right in the order of:

Tenths
Hundredths
Thousandths
Ten-thousandths

For case, the place value of 5 in 0.25 is hundredths. Follow the below table to learn the place value of digits in a number.

Hundreds

Tens

Ones

Decimal

Point (.)

Tenths

Hundredths

Thousandths

X-thousandths

Operations on Decimal Fractions

As we know, in that location are four basic operations in Maths viz. addition, subtraction, multiplication and division.

It is piece of cake to perform arithmetic operations on decimal fractions. Let us hash out the different operations performed on decimal fractions.

Addition of Decimal fractions

Suppose we need to add 2/100 and 3/10000. And so first nosotros can simplify and write in decimal fraction form.

ii/100 = 0.02

3/10000 = 0.0003

Now, adding the two values we accept:

0.02 + 0.0003 = 0.0203

Thus, we tin come across, information technology is easy to add together the fractions after writing them in decimal grade.

Subtraction of Decimal fractions

The method of subtraction of decimal fractions is the aforementioned as addition. Let united states empathize by an case.

Subtract 0.008 and 0.002.

0.008 – 0.002 = 0.006 (By subtracting the digits at the thousandths identify)

Multiplication of Decimal Fractions

When we multiply a decimal fraction by multiples of ten, so we take to shift the decimal bespeak to the right in as many places as the ability of 10.

Example: Multiply 0.089 x 100

0.089 ten 100 = eight.9

Partition of Decimal Fractions

When nosotros separate a decimal fraction by a whole number, and so remove the decimal and carve up it. Now, place the decimal point as many places as of the dividend.

Example: 0.081 ÷ 3

Remove the decimal point from 0.081 and and then carve up by 3.

81/three = 27

Now identify the decimal bespeak up to three places of decimal.

0.081/3 = 0.027

Information technology is the required answer.

Types of Decimal Fractions

The decimal fractions as discussed are the fractions whose denominators are in the multiples of ten. We have learned the types of decimals in Mathematics, such every bit:

Terminating Decimals – has a finite number of digits after the decimal
Non-Terminating Decimals – has infinite or non-terminating digits afterwards the decimal
Recurring Decimals – has repeating digits afterward the decimal
Not-Recurring Decimals – has not-repeating digits after the decimal

Based on these categories we can say, the decimal fractions are more than probable to be terminating and non-repeating. Since, the denominator here is in the power of 10 and hence, volition result in terminating decimal.

Video Lesson on Fractions

Solved Examples on Decimal Fractions

Example 1: A barrel has 56.32 litres capacity. If Supriya used 21.xix litres how much h2o is left in the barrel.

Solution: Given,

Chapters of the barrel = 56.32 liters

Amount of water used= 21.19 liters

Amount of h2o left in the barrel = 56.32 – 21.xix = 35.13 liters

Instance 2: Megha bought 12 bags of wheat flour each weighing 4563/100 kg. What volition be the full weight?

Solution:Total no. of bags = 12

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

Total weight =45.63 x 12=547.56 kg

Example 3: If circumference of a circumvolve is 16.09 cm. What will exist its diameter(π=3.14)?

Solution: Given, circumference = 16.09 cm

Circumference of a circle, C=2πr

\(\begin{assortment}{l}\Rightarrow 16.09 = 2 \pi r\end{array} \)

\(\begin{array}{l}\Rightarrow 16.09 = 2 \times 3.14 \times r\end{array} \)

\(\begin{array}{l}\Rightarrow r = \frac{16.09 \times 100}{6.28 \times 100}\end{array} \)

\(\brainstorm{array}{l}\Rightarrow r = 2.56 \end{array} \)

Therefore Diameter = 2r = two x 2.56 = five.12 cm.

Example 4: If the product of 38.46 and some other number is 658.17, what is the other number?

Solution: Given,

Ane number = 38.46

Product of two numbers = 658.17

The other number = 658.17÷38.46

\(\begin{array}{fifty}\frac{658.17}{100}\div \frac{38.46}{100}\end{array} \)

= 17.eleven

Instance 5: Rakesh bought a new. He went on a road trip of 165.9 km on wheel. After a calendar week he went for another trip of 102.04 km. What will be the reading on meter reader of the bicycle?

Solution: Given,

Altitude travelled on showtime trip = 165.nine km

Distance travelled on 2d trip = 102.04km

Total altitude travelled = 165.ix + 102.04 = 267.94 km

Practice Questions on Decimal Fractions

Write half dozen/1000 in decimal form.
What is the sum of 12/100 and 10?
Find the difference between 4/800 and 1/100.
What is the product of 18/100 and 3?

Frequently Asked Questions – FAQs

What is a decimal fraction?

A decimal fraction is a fraction with a denominator having powers of x such as 10, 100, chiliad, 10000, etc.

What is an case of a decimal fraction?

The example of decimal fractions are:
54/100 = 0.54
9/ten = 0.ix
899/1000 = 0.899

How to write a decimal into the simplest class of a fraction?

If 0.08 is a decimal, and so multiply and divide the decimal by 100.
0.08 x (100/100) = 8/100 = ii/25.

What is 0.3 as a decimal fraction?

0.3 can be written as three/10 in decimal fractions.

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