Table of contents  
Introduction  
Comparing Decimals  
Using Decimals  
Addition of Numbers with Decimals  
Subtraction of Decimals 
Decimals are an essential part of mathematics that help us represent numbers that are not whole. They are used in everyday life for things like money, measurements, and data analysis. A decimal number has two parts: a whole number and a fractional part, separated by a decimal point.
If you have 1 rupee and 50 paise, you can write it as ₹1.50. Here, 1 is the whole number (rupee), and 50 is the part of the rupee (paise) shown after the decimal point. The dot between the numbers is a decimal point, which separates rupees from paise, making it easier to work with money. So, ₹1.50 means 1 rupee and 50 paise.
Let us first understand the basics before we start comparing decimals.
(i) Converting Fractions to Decimals:
To convert a fraction to a decimal, make the denominator 10, 100, etc.
Example: Convert to a decimal
Multiply both the numerator and denominator by 5 to make the denominator 10:
So, in decimal form.
(ii) Converting Decimals to Fractions:
To convert a decimal to a fraction, place the decimal number over 10, 100, etc., depending on the number of digits after the decimal point.
Example: Convert 8.9 to a fraction
(iii) Any two decimal numbers can be compared by comparing their whole part and decimal parts.
Let us understand this by comparing 0.07 and 0.1
Example: Which is greater: 0.3 or 0.25?
Ans: Let us solve this by imagining you have two chocolate bars, both divided into 100 equal pieces.
First bar (0.25):
 You have 25 pieces out of 100.
 This represents
Second bar (0.3):
 You have 30 pieces out of 100.
 This represents
Since 30 pieces are more than 25 pieces, 0.3 is greater than 0.25.
(iv) Comparing Decimals with the Same Whole Number
Let's compare two numbers: 45.78 and 45.7. Here's how to do it step by step:
Since the whole part (45) and the tenths place (7) are equal, we move to the hundredths place:
45.78 has 8 in the hundredths place.
45.7 has 0 in the hundredths place (or 45.70).
Therefore, 45.78 > 45.7 because the hundredths part of 45.78 is more.
Even if the whole and tenth parts of two numbers are the same, you must compare the next digit (hundredth place) to find out which number is greater. In this example, 45.67 is greater because it has a larger hundredths value than 45.6.
Example: Compare 64.24 and 64.205
Ans:
Working with decimal numbers is essential when handling money, especially in cases where we need to convert paisa into rupees.
100 paise = ₹1
Therefore, 1 paise = ₹0.01
If we have to convert 5 paise to rupees, divide by 100.
For example, if we visit a local shop to purchase 500 grams of turmeric, and 1 kg of turmeric costs Rs. 51, we need to determine how much to pay the shopkeeper. By dividing Rs. 51 by 2, we get Rs. 25.5. To pay the correct amount, we need to understand what Rs. 25.5 represents in rupees. Let's explore this through a simple example.
Rs 1 = 100 paisa
Rs 0.5 = 50 paisa
Rs. 25.5 = Rs. 25 and 50 paisa
Q1: Convert 165 paisa to rupees.
Ans: Since 1 paisa = Rs. 1/100,
165 paisa = Rs. 165 × (1/100) = Rs. 165/100 = Rs. 1.65, which equals
Rs. 1 and 65 paisa.
Q2: Convert 350
Ans: Since 1 paisa = Rs. 1/100,
350 paisa = Rs. 350 × (1/100) = Rs. 350/100 = Rs. 3.50, which equals
Rs. 3 and 50 paisa.
When measuring the length of an item, it's not always the case that the length will be a multiple of the scale's markings.
For example, when using a meter scale to measure the length of a table, the measurement might not be a whole number and could fall between two markings on the scale. In such cases, decimal numbers are used.
From unit conversion, we know:
If the length of the tabletop is 2 meters and 75 centimeters, it can be represented as (2 + 75/100) meters.
Q1: Convert 5 km and 75 m into decimal.
Ans: As we know, 1 km = 1000 m
So, 1 m = 1/1000 km
5 km + 75 m = 5 + (75 × 1/1000) km = 5.075 km
Q2: Convert 61km and 25m into decimal.
Ans:
Convert meters to kilometers:
Add the kilometers:
Decimal numbers are commonly used when dealing with weight.
For example, when purchasing a watermelon, its weight might not be a whole number; it could be more than 1 kg but less than 2 kg. In such cases, the shopkeeper needs to calculate the price based on the exact weight of the watermelon. As we know:
Now, if the watermelon weighs 1 kg and 750 g, the shopkeeper will charge for 1 kg plus (750/1000) kg of watermelon. We'll explore more about converting weight into decimals through the following example:
Q1: Convert 250 g to kg.
Ans: Since 1000 g = 1 kg,
1 g = 1/1000 kg,
250 g = 250 × (1/1000) kg = 250/1000 kg = 0.250 kg.
We know that 1 g = $\frac{1}{1000}\backslash frac\{1\}\{1000\}$kg.
So, 396 g = $\frac{396}{1000}\backslash frac\{396\}\{1000\}$kg.
Therefore, 5 kg + 0.396 kg = 5.396 kg.
Steps for Addition of Numbers with Decimals:
Example: Add 0.56 + 9 + 6.287
To add decimals, line up the decimal points vertically and fill in 0's as shown:
Q1: The total weight of a box containing 14kg750g of mangoes, 5kg 80g of apples is 22kg 200g. How much is the weight of the empty box?
Ans: Weight of mangoes =14kg750g
Weight of Apples =5kg80g
Total weight of box =22kg200g
So, the weight of empty box = total box weight  total weight of fruits
Q2: Add 27.076 + 0.55 + 0.004
Ans: 27.076 + 0.55 + 0.004
It can be written as 27.076 + 0.550 + 0.004 = 27.630
Q3: Nasreen bought 3 m 20 cm cloth for her shirt and 2 m 5 cm cloth for skirt. Find the total cloth bought by her.
Ans: Cloth bought by Nasreen for shirt = 3 m 20 cm = 3.20 m
Cloth bought by Nasreen for skirt = 2 m 50 cm = 2.05 m
So the total cloth bought by her = 3.20 + 2.05 = 5.25 m = 5 m 25 cm
Hence, the total cloth bought by her is 5 m 25 cm.
⇒22kg 200 g  19 kg 830 g = 2k
Steps for Subtraction of Numbers with Decimals:
Example: Subtract 6 – 2.25
To subtract decimals, line up the decimal points vertically and add 0's where shown. Remember to borrow when necessary.
Q1: Ganesh purchased a book worth Rs.156.65 from a bookseller and he gave him Rs.500 note. How much balance did he get back?
Ans: Cost of book = Rs. 156.65
Total amount given by Ganesh = Rs. 500
So, the balance given by the shopkeeper is Rs 343. 35
Q2: Subtract 27.56 from 52.1
Ans: By subtracting 27.56 from 52.1
52.10−27.56=24.54
Therefore, we get 24.54 on subtracting 25.76 from 52.1
94 videos347 docs54 tests

1. How do you compare decimals? 
2. How can decimals be used in real life situations? 
3. How do you add numbers with decimals? 
4. What is the importance of understanding decimals in mathematics? 
5. Can decimals be subtracted using the same method as whole numbers? 

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