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Chapter 8 – Decimals

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

You may have often come across a scenario when out shopping your parents that, while purchasing cloth they ask for 1 meter and 500 centimetres, more commonly, 1.5 meters. The dot between the numbers represents a decimal point, let’s take a journey into the introduction to decimals.

We know that 10mm. = 1cm. when represented as a fraction can be denoted as:

1mm =  \frac{1}{10} cm or one-tenth of a centimeter.

In terms of decimals, this would mean that 1mm is 0.1cm

Now, let’s practice with an example: 

How would 9cm and 6mm be written as a decimal?

9 \frac{6}{10} cm which can be represented as 9.6cm.

The tenths table can be expressed as follows for a better understanding:

ExampleTens (10)Ones (1)Tenths ( \frac{1}{10})
30.6306
22.3223

Decimals on the Number Line

Let’s take a look at what decimals look like on the number line. We have written numbers from 0-1.3 on the number line. Now try continuing till the number 3.

Using 10 as the denominator makes the conversion of fractions to decimals pretty simple. Let’s learn how denominators other than 10 can be converted to decimals.

1)  \frac{13}{5} is  \frac{26}{10} which can be further simplified as  \frac{20+6}{10},  \frac{20}{10} +  \frac{6}{10}= 2+  \frac{6}{10}

= 2.6

Quick exercise: Write  \frac{1}{2}in decimal form

Decimals as Fractions

And now let us reverse what we had learned earlier for converting fractions to decimals. This is how we write 1.5 as a fraction;

1+ \frac{5}{10},  \frac{10}{10}+  \frac{5}{10}=  \frac{15}{10}

We learned in the first half of the chapter how decimals can be written in terms of 10’s, but what if they were to be represented as 100’s? Let’s take the example of metres and centimetres. We know that 1m. = 100cm., therefore 1cm. =  \frac{1}{100}m.

In decimals this is expressed as 1cm. = 0.01m. 

Similarly, any fraction whose denominators are in hundredths or thousandths can be expressed this way. 

Take a look at this table with examples for a better understanding:

Ones (1)Tenths ( \frac{1}{10})Hundredths ( \frac{1}{100})
0.02002
0.15015

0.4, 0.08

Here are two numbers with decimals, can you tell which is greater?

In terms of ones both the numbers are equal (0), however, in terms of tenths 0.4 (4) is greater than 0.08 (0). 

Hence, 0.4>0.08. You can attempt this with numbers such as 1.25, 1.02, or 67.91, 67.90.

While comparing decimals it is important you take into consideration all the digits after the decimal point

Decimals have applications in various measurements used in our day to day lives. Let’s take a look at how they are used:

  • Money

You know that 1 rupee = 100 paise. This can be expressed using decimals as 1 paisa is 0.01 rupees. Similarly, 80 paise can be written as 0.80 rupees. 

But how do you express 206 paise? 206 paise is 2 rupees and 6 paise and can be written as 2.06.

  • Length

Determining the length of items is present in your house or the distance between two points is another place where using decimals is possible. 

For example, let’s say you want to express 175cm in terms of meters. We know that 1m = 100cm, so 175cm can be expressed as 1.75m.

  • Weight

You go to the market and purchase 500g rice, 500g wheat, 300g spices, and 600g dal. This means that you have made a total purchase of 1900g in weight. How would this be represented in kilograms?

 We know that 1kg. = 1000g. That is 1g = 0.001kg.

 Therefore, 1900g. can be expressed as 1.9kg.

Addition of numbers with decimals is quite similar to the addition of regular numbers. Let’s see how the numbers 0.56 and 0.92 can be added using a table.

OnesTenthsHundredths
056
092
148

=1.48

Hence, 0.56+0.92= 1.48

Let’s understand this better with a word problem, say you travel 17km 600m by bus, 6km 400m by car and 800m on foot. How much distance would you have traveled?

Let’s take this step-by-step:

  • By bus- 17km. 600m. or 17.6km.
  • By car- 6km. 400m. or 6.4km.
  • By foot- 800m. or 0.8km.

Total distance travelled equals:

17.6+6.4+0.8

= 24.8 km

Like addition, subtraction of decimals can be done by subtracting ones from ones, tenths from tenths, and so on. You may also need to borrow units as in the case of regular subtraction. Take a look at this table in which we subtract 1.93 from 4.65;

OnesTenthsHundredths
465
193
372

=3.72

Therefore, 4.65-1.93= 3.72

1. What are the 3 types of decimals?
The three types of decimals are:

  • Terminating: These are decimals that have a limited or finite number of digits after the decimal. For example,  \frac{1}{2} in decimal can be written as 0.5. Hence, it is a terminating decimal with finite numbers after the decimal.
  • Recurring: They are numbers with either one or more repeating digits that do not terminate. It means that this sequence of numbers after the decimal is infinite. For example,  \frac{1}{6} as a decimal is 0.166666… it can also be written as 0.16.
  • Irrational numbers: These are numbers that do not form repeating sequences and are infinite. They cannot be expressed in a fraction. For example, 2.71828182845904…

2. How do you do decimals in math?

Decimals can be solved like regular numbers; the only difference is emphasizing the position of the decimal point. For example, multiplying 0.15 by 10 would result in moving the decimal point one place right, which means the number would now be 1.5. Similarly, dividing 1.5 by 10 would move the decimal one place left giving 0.15.

3. How do beginners learn decimals? 

Beginners can learn decimals with the help of a tutor or using online education apps such as MSVgo which is a video library that fosters an understanding of complex concepts with the help of a visual learning experience. 

4. How do you figure out decimals?

You can understand Decimals with the help of apps such as MSVgo that will help you grasp the concept from scratch with their informative videos and learning content, making you an expert in the subject.

5. Is 0.75 a terminating decimal? 

Yes, as it has a finite number of digits after the decimal point.

6. What is 3/8 in a decimal?

 \frac{3}{8} in decimal can be expressed as 0.375.

Decimals can be a complex math concept and you must understand it clearly to ensure an excellent math record. We at MSVgo, help you understand it right from the introduction of decimals to difficult concepts in various subjects with videos that are easy to understand, engaging, and explanatory. Visit our website to know more.

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