Representing Decimals on a Number Line: What You Need to Know

One may think that it would be difficult to locate a decimal number on a number line. But, it is simpler as locating any whole number on the number line. Yes, a little bit more effort will be required; however, it is not difficult at all.

To start, let us consider an example such as 3.68 on the number line. Now, looking at the decimal number 3.6, you would easily understand that it lies between the whole numbers three and four.

So an obvious thing to do is first mark the points 3 and 4 and divide the segments between them. 

Divide the segments between the whole numbers 3 and 4 such that there are 100 equal parts to represent 3.61, 3.62. 3,63…and so on. We are doing this as we are talking about the 100th place of two decimal numbers.

In our case, remember that each small division is equivalent to 0.01.

When you begin from 3, keep moving 68 such small steps on the decimal divisions between 3 and 4 until you reach .68-->that will be 3.68.

Alternatively, there is another way of doing it, and that is we have to divide or draw segments of ten equal parts. This is because we are dealing with 10 parts (tenths) first. Then, later, we will look upon subdividing each of those tenth parts further into hundredths, etc.

This technique will aid us in visualizing that 3.68 is much closer to 4 when compared to 3. Specifically put, 3.10 is just a little ahead of 3, etc.

Hence, it is always recommended to draw numbers on a number line with divisions (segments) on it. This helps in understanding which decimal number is closer to which whole number. 

Simply put: start by marking 3.0, then 3.1, 3.2, … 3.9, 4.0. To be more precise, inside 3.6 to 3.7, you need to place 3.68 a bit after 3.6, plus 8 subdivisions.

Table of Contents
•    Numerical: Fraction to Decimal Conversion: The Methods Step by Step
•    Expansion Format: From Decimal to Fraction
•    F&Qs Related to Decimal Numbers
•    F&Qs With Answers Related to Decimal Numbers
•    Numerical Problems Based on Addition and Subtraction of Decimal Numbers
•    Summary of Decimal Numbers: What They Are and Their Uses in Different Fields

Fractions ↔ Decimals: How to Perform Interconversion
In mathematics, it is very common that you have to convert fractions to decimals as when needed. This is done so that we can understand the precise value that is needed for any particular purpose, such as nursery length.

Let us take examples to understand how the interconversion is carried out between the fractions and the decimals.

Another reason is that many ideas in mathematics have to be expressed in cross fractions and decimals. This is the reason why we need to know how to convert:

Numerical: Fraction to Decimal Conversion: The Methods Step by Step 

Q1: You will have to convert the fraction 5/20 to decimal form. Show all steps needed to perform the decimal form conversion. 
A1: To begin, we need to ask ourselves: can we make the denominator such that it turns into a power of 10? 20 = 2 × 10. For the same, you need to multiply the top as well as the bottom by the number 5. This, when performed, will make the denominator 100:
Hence the fraction 5/20 = (5×5)/(20×5) = 25/100 = 0.25.
Or, you can do long division: 5 ÷ 20 = ¼= 0.25 exactly.
Q2: Convert the fraction 2/8 to decimal form. Show all steps needed to perform the decimal form conversion.
A2: You can opt for the long division method in this case: 2/8 = ¼ = 0.25 exactly.

Expansion Format: From Decimal to Fraction
Expand the decimal number 8.82 = 8 + 0.82 = (800/100) + (82/100) = (800 + 82)/100 = 882/100 = simplify divide by 42 in numerator and denominator → 221/25.
Or you can directly divide 221/100 = 2.21.
You have to be careful as you need to check if the decimal terminates. A trick that you can use is that you can express the given fraction (with a denominator) as some power of 10.
In such cases, decimal repeats, then you perform an algebraic trick. With this, you may end up with an equivalent fraction.

F&Qs Related to Decimal Numbers
1.    Explain the meaning of decimal numbers and how it is different from whole numbers?
Answer 1: Decimal numbers are different from whole numbers as they are represented by putting a dot after the whole number. Whatever digits appear after the decimal point are called the decimal digits. 

Consider 2.35; Here, two is the whole number, and after the decimal point, you can notice that 35 are the digits; they are called the decimal part. 

2. Why does it make sense to compare the decimal numbers place by place?

Answer 2: This is done as digits in different places have their own face value or names. The digit after the decimal point is in the tenth place, then comes the hundredths, thousandths, and so on. This is the reason why comparison must follow place‐by‐place order.

3. When does it become necessary to write trailing zeros in decimal numbers--give your explanation. 

Answer 3. The concept of using the trailing zero is done only to align places. For example, consider the decimal number 4.50. In such a case, 4.5 can also be written in place of 4.50. Thus, it has to be noted that the introduction of zeros does not change the value of the decimal number.

4. How can we convert decimals when it comes to fractions?
Answer 4: You will have to write a decimal in the form of a number with a power of ten. An e.g. best could be: 3.72 = 372/100, then, it can be simplified by using the method of division.
5. Where can you think of using decimals in regards to real life?
Answer 5: The most common situations are: while using money (₹ 12.75), carrying out measurement (2.35 m), taking medicine (0.125 mg), developing engineering drawings, etc.

F&Qs With Answers Related to Decimal Numbers

1. Explain the meaning of decimal numbers and how it is different from whole numbers.
Answer 1: Decimal numbers are different from whole numbers as they are represented by putting a dot after the whole number. Whatever digits appear after the decimal point are called the decimal digits.
Consider 2.35; Here, two is the whole number, and after the decimal point, you can notice that 35 are the digits; they are called the decimal part.

2. Why does it make sense to compare the decimal numbers place by place?
Answer 2: This is done as digits in different places have their own face value or names. The digit after the decimal point is in the tenth place, then comes the hundredths, thousandths, and so on. This is the reason why comparison must follow place‐by‐place order.

3. When does it become necessary to write trailing zeros in decimal numbers--give your explanation.
Answer 3. The concept of using the trailing zero is done only to align places. For example, consider the decimal number 4.50; in such a case, 4.5 can also be written in place of 4.50. Thus, it has to be noted that the introduction of zeros does not change the value of the decimal number.

4. How can we convert decimals when it comes to fractions?
Answer 4: You will have to write a decimal in the form of a number with a power of ten. An e.g. best could be: 3.72 = 372/100, then, it can be simplified by using the method of division.

5. Where can you think of using decimals in regards to real life?
Answer 5: The most common situations are: while using money (₹ 12.75), carrying out measurement (2.35 m), taking medicine (0.125 mg), developing engineering drawings, etc.

Numerical Problems Based on Addition and Subtraction of Decimal Numbers 
Problem 1. Among the two
, which decimal is larger: 5.234 or 5.243?
Answer: Check whole parts, that is 5, and move on to compare tenths. You would notice both have 2 tenths (0.2). Then, next, you will have to move to hundredths. In 5.234, you will notice that there are 3 hundredths (0.03); 5.243 has 4 hundredths (0.04). When comparison is done between 0.04 and 0.03, .04 > 0.03. and hence, 5.243 > 5.234.
Problem 2. Add the decimal numbers that are 4.56 and 3.789.
Answer: When both decimal numbers are added, we get:
4.560
+ 3.789
= 8.349
Rounding off 4.56 as 4.560 is done to match three decimal places. So carrying on the addition, we get the thousandths: 0 + 9 = 9; hundredths: 6 + 8 = 14 → write 4 carry 1; tenths: 5 + 7 + carry 1 = 13 → write 3 carry 1; whole part: 4 + 3 + carry 1 = 8. So the addition results in 8.349.
Problem 3. Subtract teh decimal numbers that are 5.002 – 3.478.
Answer: Initially, you will have to align tthe decimal numbers and they are:
5.002
– 3.478
You will have to borrow from 5.002: the 0 in hundredths borrows from 0 in tenths. Then, borrowing from the 5 in units has to be done. Ultimately, we get:
5.002 can be thought as 4. (tens/hundreds) → after cascaded borrowing, you get 4. (something). Also, rounding off 5.002, we get 5.0020 and
3.478 = 3.4780.
Now carry out the subtraction, and you will find 1.524.
Alternatively: you can also do: 5.002 − 3.478 = (5.002 − 3.478) = 1.524 (verify by adding 3.478 + 1.524 = 5.002).

Summary of Decimal Numbers: What They Are and Their Uses in Different Fields
1.    Decimal numbers come in very handy when numbers have to be dealt with non-whole values. This means we have to deal with numbers that do not represent only whole numbers but also decimal values. 

2.    The concept of a decimal number is devised in such a way that the decimal part splits the entire number into 2 parts. These are whole parts plus the fractional part through the use of the signal point. 

When it comes to decimal numbers, they're named according to their places, and they are: tenths, hundredths, thousandths, etc.

3.    When it comes to comparison, it makes sense to first compare the presence of whole parts, then come the tenths, then comparison with hundredths, then further.

4.    It has to be understood that even decimals can come put in a number line for understanding purposes by dividing intervals between two whole numbers.

5.    When it comes to the conversion of fractions to decimals, it is very much possible by making the denominator a power of 10 and the other way round too.

6.    Coming to the use of decimals, they can be used for understanding money dealings, measurement problems, engineering, where precise values are required, medicine, where a small extra quantity of some chemical may affect patients, and various other industries.