Chapter 3
A Peek Beyond the Point
Measurement is an important part of our daily life. Sometimes whole
numbers are not enough to describe the exact length, height or
distance of an object. In this chapter, we learn how smaller units
help us measure more accurately and introduce the concept of
tenths and decimal numbers.
Introduction
Imagine you are measuring the length of a pencil using a ruler.
Sometimes the pencil ends exactly at a whole centimetre mark,
but many times it ends somewhere between two marks.
In such situations, whole numbers cannot describe the measurement
accurately. We need smaller parts of a unit to express the exact
length.
This idea leads us to decimal numbers, where one unit is divided
into smaller equal parts.
Learning Objectives
- Understand why smaller units are needed.
- Measure objects more accurately.
- Learn about parts of a whole unit.
- Relate fractions with measurements.
- Prepare for learning decimal numbers.
Why Do We Need Smaller Units?
Definition
A smaller unit is a part of a standard unit that helps us
measure objects more precisely when whole units are not
sufficient.
Suppose the length of a ribbon is greater than 5 cm but less
than 6 cm. If we only write 5 cm or 6 cm, the measurement is
not accurate.
Therefore, we divide one centimetre into smaller equal parts.
This helps us express the exact measurement.
Examples from Daily Life
Example 1
A pencil measures a little more than 12 cm.
We need smaller units to find its exact length.
Example 2
A mobile phone is longer than 15 cm but shorter than
16 cm.
Example 3
The width of a notebook is between 20 cm and 21 cm.
Example 4
A table is about 1 metre long, but the exact length
requires smaller units.
Real-Life Applications
Shopping
Cloth is measured using metres and centimetres.
Construction
Engineers measure buildings using accurate units.
Science
Scientists use very small units for precise observations.
Sports
Race timings and distances require exact measurements.
Remember
Measuring only with whole numbers may not always give an
accurate answer. Dividing a unit into smaller equal parts
allows us to express measurements more precisely.
3.2 Units of Measurement
Measuring accurately is important in everyday life. Different objects have
different sizes and weights, so we use standard units to measure them.
Sometimes we also need to convert one unit into another for easier
calculation.
What is a Unit?
A unit is a fixed quantity used as a standard for measuring length,
weight, capacity, time, or any other physical quantity.
Length Measurement
Length tells us how long or short an object is. Small objects are usually
measured in millimetres (mm) or centimetres (cm), while longer distances
are measured in metres (m) or kilometres (km).
| Unit |
Symbol |
Used For |
| Millimetre |
mm |
Thickness of paper, coins |
| Centimetre |
cm |
Pencil, Notebook |
| Metre |
m |
Door, Table, Room |
| Kilometre |
km |
Distance between cities |
Important Length Conversions
Worked Examples
Example 1
Convert 8 cm into millimetres.
1 cm = 10 mm
8 × 10 = 80 mm
Example 2
Convert 250 cm into metres.
250 ÷ 100
=2.5 m
Example 3
Convert 5 km into metres.
5 × 1000
=5000 m
Weight Measurement
Weight tells us how heavy or light an object is.
| Unit |
Symbol |
Example |
| Milligram |
mg |
Medicine |
| Gram |
g |
Chocolate |
| Kilogram |
kg |
Rice Bag |
Money Measurement
Money is also represented using decimal values.
| Money |
Decimal Form |
| 50 Paise |
₹0.50 |
| 25 Paise |
₹0.25 |
| 75 Paise |
₹0.75 |
| 150 Paise |
₹1.50 |
Real-Life Applications
Shopping
Fruit is weighed in kilograms.
Tailoring
Cloth is measured in metres.
Medical Field
Medicines are measured in milligrams.
Travel
Road distances are measured in kilometres.
Quick Tip
Always convert all quantities into the same unit before performing
addition or subtraction.
Practice Questions
- Convert 6 cm into millimetres.
- Convert 350 cm into metres.
- Convert 4 kg into grams.
- Convert 8500 m into kilometres.
- Write 75 paise in decimal form.
- Convert ₹3.25 into paise.
Quick Quiz
1.
1 metre = ?
A. 10 cm
B. 100 cm ✅
C. 1000 cm
D. 1 cm
2.
1 kilogram =
A. 100 g
B. 500 g
C. 1000 g ✅
D. 10 g
3.
50 paise is equal to
A. ₹5
B. ₹0.5 ✅
C. ₹50
D. ₹0.05
Part Summary
- Standard units help us measure accurately.
- Length is measured in mm, cm, m and km.
- Weight is measured in mg, g and kg.
- Money uses decimal notation.
- Convert units before comparing or calculating.
3.3 Understanding Decimal Numbers
Whole numbers are useful in many situations, but they cannot always
describe exact measurements. For example, if the length of a notebook
is more than 12 cm but less than 13 cm, writing only 12 cm or 13 cm
is not accurate.
To represent such measurements, we divide one whole unit into smaller
equal parts. These parts can be written using decimal numbers.
Definition
A decimal number represents a whole number together with one or
more parts of a whole. The decimal point separates the whole part
from the fractional part.
Decimal Point
The decimal point (.) is a special symbol used to separate the whole
number from its smaller parts.
| Number |
Whole Part |
Decimal Part |
| 4.5 |
4 |
5 Tenths |
| 8.25 |
8 |
25 Hundredths |
| 12.75 |
12 |
75 Hundredths |
Tenths
When one whole is divided into ten equal parts, each part is called
one tenth.
1 Whole = 10 Tenths
1 Tenth = 0.1
Hundredths
If one whole is divided into one hundred equal parts,
each part is called one hundredth.
1 Whole = 100 Hundredths
1 Hundredth = 0.01
| Fraction |
Decimal |
| 5/100 |
0.05 |
| 12/100 |
0.12 |
| 45/100 |
0.45 |
| 99/100 |
0.99 |
Place Value in Decimal Numbers
Every digit in a decimal number has a place value depending on its
position.
| Thousands |
Hundreds |
Tens |
Ones |
Tenths |
Hundredths |
| 0 |
0 |
3 |
5 |
4 |
8 |
In the decimal number
35.48:
- 3 is in the Tens place.
- 5 is in the Ones place.
- 4 is in the Tenths place.
- 8 is in the Hundredths place.
Reading Decimal Numbers
18.45
Eighteen and Forty-five Hundredths
100.08
One Hundred and Eight Hundredths
Decimal Numbers on a Number Line
Decimal numbers can also be represented on a number line.
Each interval between two whole numbers can be divided into
ten equal parts to show tenths.
0 ─┬─┬─┬─┬─┬─┬─┬─┬─┬─┬── 1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Real-Life Uses of Decimal Numbers
Shopping
Product prices are written in decimal form.
Sports
Race timings are measured using decimals.
Medicine
Medicine quantities are often written as decimals.
Science
Precise measurements require decimal values.
Remember
Every digit after the decimal point has a place value.
The first digit represents tenths, while the second digit
represents hundredths.
Comparing Decimal Numbers
Comparing decimal numbers is similar to comparing whole numbers.
First compare the whole number part. If they are equal, compare
the digits after the decimal point from left to right.
Rule to Compare Decimals
- Compare the whole number part.
- If equal, compare the tenths digit.
- If still equal, compare the hundredths digit.
- The first larger digit determines the greater number.
Examples
Example 1
Compare 5.7 and 5.4
Whole numbers are equal.
7 tenths > 4 tenths
5.7 > 5.4
Example 2
Compare 12.35 and 12.53
Whole numbers are equal.
3 tenths < 5 tenths
12.35 < 12.53
Example 3
Compare 8.48 and 8.45
Tenths are equal.
8 hundredths > 5 hundredths
8.48 > 8.45
Ordering Decimal Numbers
Arrange decimal numbers by comparing each value carefully.
| Numbers |
Ascending Order |
| 4.8, 4.3, 4.6 |
4.3, 4.6, 4.8 |
| 7.25, 7.05, 7.5 |
7.05, 7.25, 7.5 |
| 2.11, 2.09, 2.9 |
2.09, 2.11, 2.9 |
Equivalent Decimal Numbers
Adding zeros to the right side of a decimal number does not change
its value.
Common Mistakes
❌ Mistake
Thinking 4.25 is greater than 4.8 because 25 is greater than 8.
✅ Correct
Compare the tenths first.
4.8 = 4.80
80 hundredths > 25 hundredths.
❌ Mistake
Ignoring the decimal point.
✅ Correct
Always compare place values.
Practice Questions
- Which is greater: 6.8 or 6.5?
- Arrange 3.2, 3.09 and 3.25 in ascending order.
- Write the larger number: 9.15 or 9.51.
- Are 7.4 and 7.40 equal?
- Arrange 12.08, 12.8 and 12.18 in descending order.
- Compare 15.35 and 15.305.
Quick MCQs
1.
Which number is greater?
A. 5.09
B. 5.9 ✅
C. Equal
D. Cannot say
2.
7.40 is equal to
A. 7.4 ✅
B. 7.04
C. 74
D. 0.74
3.
Which is smallest?
A. 8.6
B. 8.06 ✅
C. 8.60
D. 8.600
4.
Arrange in ascending order.
A. 2.3, 2.13, 2.31
B. 2.13, 2.3, 2.31 ✅
C. 2.31, 2.3, 2.13
D. 2.3, 2.31, 2.13
Part Summary
- Compare the whole number first.
- If whole numbers are equal, compare tenths.
- Then compare hundredths if needed.
- Trailing zeros do not change the value of a decimal.
- Always compare place values instead of counting digits.
Exam Tip
Convert decimals to the same number of decimal places before comparing.
For example:
5.4 → 5.40
5.38 → 5.38
Now comparison becomes much easier.
3.4 Addition and Subtraction of Decimal Numbers
Decimal numbers are added and subtracted in almost the same way as
whole numbers. The most important rule is to keep the decimal points
exactly below one another before performing any calculation.
Important Rule
Write the decimal numbers in one column so that the decimal points
are aligned. Then add or subtract digit by digit from right to left.
Steps for Adding Decimal Numbers
- Write the numbers vertically.
- Align the decimal points.
- Add digits from right to left.
- Write the decimal point directly below the others.
Solved Examples - Addition
Example 1
4.25
+ 2.30
------
6.55
Answer: 6.55
Example 2
12.75
+ 5.20
-------
17.95
Answer: 17.95
Example 3
0.85
+1.15
------
2.00
Answer: 2.00
Steps for Subtracting Decimal Numbers
- Arrange the numbers vertically.
- Keep decimal points in one straight line.
- Subtract from right to left.
- Borrow when required.
Solved Examples - Subtraction
Example 1
8.50
-3.20
------
5.30
Example 2
15.75
-4.50
------
11.25
Example 3
20.00
-7.85
------
12.15
Word Problems
Shopping
A notebook costs ₹45.50 and a pen costs ₹18.25.
Find the total amount.
Answer: ₹63.75
Distance
Rahul walked 3.75 km in the morning and
2.40 km in the evening.
Total = 6.15 km
Weight
A bag weighs 12.80 kg.
After removing 2.35 kg, what is the remaining weight?
Answer = 10.45 kg
Common Mistakes
- ❌ Writing decimal points in different positions.
- ❌ Forgetting to write zero when required.
- ❌ Ignoring place values.
- ✅ Always align decimal points carefully.
Quick Tip
If one number has fewer decimal places,
add zeros to make both numbers have the same
number of decimal digits before calculating.
Practice Questions
- 4.25 + 5.75 = ?
- 18.50 + 2.35 = ?
- 12.80 − 5.25 = ?
- 25.00 − 7.85 = ?
- Find the total of ₹18.75 and ₹24.50.
- A rope is 15.50 m long. If 6.75 m is cut, what length remains?
Quick Quiz
1.
5.50 + 2.25 = ?
A. 7.50
B. 7.75 ✅
C. 8.25
D. 6.75
2.
15.80 − 4.20 = ?
A. 10.60
B. 11.60 ✅
C. 12.00
D. 10.40
3.
Which rule is most important while adding decimals?
A. Count digits
B. Align decimal points ✅
C. Multiply first
D. Ignore zeros
Part Summary
- Always align decimal points before calculation.
- Add and subtract just like whole numbers.
- Write the decimal point directly below the others.
- Use zeros where necessary to maintain place value.
- Decimal operations are useful in money, length, weight and daily calculations.
Chapter Revision
Before attempting the exercises, revise the important ideas from this
chapter. Understanding these concepts will help you solve decimal
problems quickly and accurately.
Quick Revision of Concepts
Decimal Numbers
Decimal numbers represent values between whole numbers.
They are useful for measuring length, weight, money,
temperature and many real-life quantities.
Tenths
The first digit after the decimal point represents
tenths.
Example: 4.7 → 7 tenths
Hundredths
The second digit after the decimal point represents
hundredths.
Example: 8.45 → 45 hundredths
Equivalent Decimals
Adding zeros to the right side of a decimal does not change
its value.
Example: 6.5 = 6.50 = 6.500
Important Formulae & Facts
Place Value Table
| Number |
Units |
Tenths |
Hundredths |
| 5.3 |
5 |
3 |
0 |
| 8.47 |
8 |
4 |
7 |
| 12.09 |
12 |
0 |
9 |
Rules to Remember
- Always compare the whole number first.
- If whole numbers are equal, compare tenths.
- If tenths are equal, compare hundredths.
- Align decimal points before addition or subtraction.
- Write extra zeros if needed.
- Do not ignore the place value of digits.
Quick Examples
Addition
4.25 + 2.50 =
6.75
Subtraction
10.50 − 3.75 =
6.75
Equivalent Decimal
9.4 = 9.40
Real-Life Uses of Decimals
Shopping
Prices of products are written using decimal numbers.
Measurement
Length, height and distance often use decimals.
Weight
Weights of fruits and vegetables are measured using decimals.
Science
Temperature and laboratory measurements use decimal values.
Exam Tips
- Read every decimal carefully.
- Keep decimal points in one vertical line.
- Do not compare only the number of digits.
- Practice word problems regularly.
- Always check your final answer.
Revision Summary
- Decimals help represent parts of a whole.
- Every digit has a fixed place value.
- Tenths and hundredths are the most common decimal places.
- Equivalent decimals have the same value.
- Decimal operations follow the same rules as whole numbers.
- Decimals are widely used in everyday life.
Chapter Revision
Before attempting the exercises, revise the important ideas from this
chapter. Understanding these concepts will help you solve decimal
problems quickly and accurately.
Quick Revision of Concepts
Decimal Numbers
Decimal numbers represent values between whole numbers.
They are useful for measuring length, weight, money,
temperature and many real-life quantities.
Tenths
The first digit after the decimal point represents
tenths.
Example: 4.7 → 7 tenths
Hundredths
The second digit after the decimal point represents
hundredths.
Example: 8.45 → 45 hundredths
Equivalent Decimals
Adding zeros to the right side of a decimal does not change
its value.
Example: 6.5 = 6.50 = 6.500
Important Formulae & Facts
Place Value Table
| Number |
Units |
Tenths |
Hundredths |
| 5.3 |
5 |
3 |
0 |
| 8.47 |
8 |
4 |
7 |
| 12.09 |
12 |
0 |
9 |
Rules to Remember
- Always compare the whole number first.
- If whole numbers are equal, compare tenths.
- If tenths are equal, compare hundredths.
- Align decimal points before addition or subtraction.
- Write extra zeros if needed.
- Do not ignore the place value of digits.
Quick Examples
Addition
4.25 + 2.50 =
6.75
Subtraction
10.50 − 3.75 =
6.75
Equivalent Decimal
9.4 = 9.40
Real-Life Uses of Decimals
Shopping
Prices of products are written using decimal numbers.
Measurement
Length, height and distance often use decimals.
Weight
Weights of fruits and vegetables are measured using decimals.
Science
Temperature and laboratory measurements use decimal values.
Exam Tips
- Read every decimal carefully.
- Keep decimal points in one vertical line.
- Do not compare only the number of digits.
- Practice word problems regularly.
- Always check your final answer.
Revision Summary
- Decimals help represent parts of a whole.
- Every digit has a fixed place value.
- Tenths and hundredths are the most common decimal places.
- Equivalent decimals have the same value.
- Decimal operations follow the same rules as whole numbers.
- Decimals are widely used in everyday life.
Part 5B – Solved Practice Questions
Practice is the best way to strengthen your understanding of decimal numbers.
The following solved examples explain each step clearly.
Solved Question 1
Write 7 tenths in decimal form.
Solved Question 2
Write 45 hundredths as a decimal.
Solved Question 3
Find the place value of digit 6 in 18.64.
Digit 6 is in the tenths place.
Place value = 0.6
Solved Question 4
Compare 9.35 and 9.53.
Whole numbers are equal.
Compare tenths:
3 < 5
9.35 < 9.53
Solved Question 5
Add 12.45 and 6.30.
12.45
+6.30
------
18.75
Answer: 18.75
Solved Question 6
Subtract 15.80 from 24.25.
24.25
-15.80
------
8.45
Answer: 8.45
Solved Question 7
Arrange in ascending order:
3.8 , 3.08 , 3.18 , 3.80
Convert for easy comparison:
3.80 = 3.8
3.08 < 3.18 < 3.80 = 3.8
Solved Question 8
Arrange in descending order:
6.42 , 6.24 , 6.04 , 6.40
6.42 > 6.40 > 6.24 > 6.04
Solved Question 9
A pencil costs ₹12.75 and an eraser costs ₹5.25.
Find the total cost.
12.75
+5.25
------
18.00
Total Cost = ₹18.00
Solved Question 10
A ribbon is 9.50 m long.
If 2.75 m is used, how much ribbon remains?
9.50
-2.75
-----
6.75
Remaining Length = 6.75 m
Number Line Practice
Question
Between which two whole numbers does 5.7 lie?
Answer:
Between 5 and 6.
Question
Between which two whole numbers does 8.25 lie?
Answer:
Between 8 and 9.
Daily Life Practice
Milk
Riya bought 2.5 litres of milk and later bought another
1.25 litres.
Total = 3.75 litres
Distance
Rahul walked 4.6 km in the morning and
3.4 km in the evening.
Total = 8.0 km
Weight
A watermelon weighs 7.80 kg.
After cutting 2.15 kg,
how much remains?
5.65 kg
Common Mistakes
- Do not compare only the number of digits.
- Always compare place values.
- Write decimal points in one straight line.
- Add zeros whenever required.
- Check the final answer carefully.
Practice Summary
- Read decimal numbers carefully.
- Understand place values before comparing numbers.
- Align decimal points for addition and subtraction.
- Practice real-life problems regularly.
- Confidence improves with regular practice.
Part 5C – Practice Exercise
Now it's your turn! Solve the following questions to test your understanding
of decimal numbers, place value, comparison, and decimal operations.
Fill in the Blanks
- 8 tenths = ________
- 35 hundredths = ________
- 1 whole = ________ tenths.
- 100 hundredths = ________.
- 6.50 = ________.
- The digit 4 in 9.45 is in the ________ place.
- The digit 8 in 12.08 is in the ________ place.
- 9.2 + 0.8 = ________.
- 15.5 − 2.3 = ________.
- 0.75 is greater than ________.
True or False
- 4.50 and 4.5 have the same value.
- 0.8 is greater than 0.75.
- 100 hundredths make one whole.
- 7.09 is greater than 7.9.
- Decimal points should always be aligned while adding decimals.
- 3.25 = 3.250
- 5 tenths = 0.05
- 9.99 is smaller than 10.
Match the Following
| Column A |
Column B |
| 0.1 |
One Hundredth |
| 0.01 |
One Tenth |
| 100 Hundredths |
1 Whole |
| ₹1 |
100 Paise |
| 1 kg |
1000 g |
Short Answer Questions
- Write 9 tenths as a decimal number.
- Write 62 hundredths in decimal form.
- Find the place value of digit 3 in 18.34.
- Compare 6.72 and 6.27.
- Arrange 4.8, 4.08, 4.18 and 4.80 in ascending order.
- Arrange 7.15, 7.05, 7.50 and 7.25 in descending order.
- Add 8.75 and 2.45.
- Subtract 12.60 from 25.75.
Long Answer Questions
-
A shopkeeper sold goods worth ₹125.75 in the morning and ₹86.40 in the evening.
Find the total sales.
-
A rope was 18.5 metres long.
After using 6.75 metres,
how much rope remained?
-
A cyclist travelled 12.75 km before lunch and 8.25 km after lunch.
Find the total distance travelled.
-
A water tank contained 50.80 litres of water.
If 18.45 litres were used,
how much water remained?
Application-Based Questions
Shopping
Rohan bought a notebook for ₹48.50 and a pen for ₹15.25.
Calculate the total amount spent.
Distance
A bus travelled 25.75 km in the morning
and 18.50 km in the afternoon.
Find the total distance.
Weight
A fruit basket weighs 12.40 kg.
After removing fruits weighing 3.65 kg,
find the remaining weight.
Measurement
A ribbon is 9.8 metres long.
If 2.35 metres are cut,
what length remains?
Challenge Yourself
- Write three decimal numbers between 5.2 and 5.3.
- Find two different decimals whose sum is exactly 10.
- Write a decimal number greater than 8.45 but less than 8.50.
- Create your own real-life problem involving decimal addition.
Practice Tips
- Read each question carefully.
- Write numbers neatly.
- Keep decimal points in one straight line.
- Check calculations after solving.
- Practice a few questions daily for better speed.
Exercise Summary
- Practice improves accuracy.
- Understand place value before comparing decimals.
- Always align decimal points in calculations.
- Decimals are useful in money, measurements, science and everyday life.
- Solve both numerical and word problems regularly.
Chapter Test - Multiple Choice Questions
Choose the correct answer for each question.
1. Which decimal represents seven tenths?
A. 7.0
B. 0.7 ✅
C. 0.07
D. 7.07
2. Which decimal is greater?
A. 5.18
B. 5.81 ✅
C. Equal
D. Cannot determine
3. 25 hundredths is equal to
A. 0.25 ✅
B. 2.5
C. 25.0
D. 0.025
4. Which decimal is equal to 9.50?
A. 9.05
B. 9.5 ✅
C. 95.0
D. 0.95
5. The digit immediately after the decimal point represents
A. Ones
B. Tenths ✅
C. Hundredths
D. Thousands
6. 8.4 + 2.6 =
A. 10
B. 10.0
C. 11.0 ✅
D. 12
7. 15.75 − 5.25 =
A. 10.50 ✅
B. 10.25
C. 9.50
D. 11.00
8. Which number is smallest?
A. 4.09 ✅
B. 4.90
C. 4.19
D. 4.99
9. 1 kilogram equals
A. 100 g
B. 1000 g ✅
C. 10 g
D. 10000 g
10. ₹1 equals
A. 10 paise
B. 50 paise
C. 100 paise ✅
D. 1000 paise
11. Which symbol separates the whole part from the decimal part?
A. Colon
B. Decimal Point ✅
C. Slash
D. Comma
12. Which is greater?
A. 12.09
B. 12.90 ✅
C. Equal
D. Cannot compare
13. 3.40 is equal to
A. 3.04
B. 3.4 ✅
C. 34
D. 0.34
14. 0.9 is equal to
A. 90 hundredths ✅
B. 9 hundredths
C. 9 thousandths
D. None
15. Arrange correctly:
A. 2.05 < 2.5 ✅
B. 2.5 < 2.05
C. Equal
D. None
16. Which is an equivalent decimal?
A. 4.8 = 4.80 ✅
B. 4.8 = 4.08
C. 4.8 = 48
D. None
17. Which operation requires decimal points to be aligned?
A. Addition ✅
B. Subtraction ✅
C. Both A and B ✅
D. Division only
18. 0.75 is between
A. 0 and 1 ✅
B. 1 and 2
C. 2 and 3
D. 5 and 6
19. Which is a decimal number?
A. 15
B. 15.5 ✅
C. XV
D. Fifteen
20. Decimal numbers are mainly used for
A. Accurate measurements ✅
B. Writing names
C. Grammar
D. Drawing
Assertion and Reason
Choose the correct option:
A. Both Assertion and Reason are true, and Reason explains Assertion.
B. Both are true, but Reason is not the correct explanation.
C. Assertion is true, Reason is false.
D. Assertion is false, Reason is true.
1.
Assertion: 4.50 = 4.5
Reason: Adding zeros to the right side of a decimal does not change its value.
Answer: A ✅
2.
Assertion: 7.08 is greater than 7.8
Reason: Tenths place is compared before hundredths.
Answer: D ✅
3.
Assertion: Decimal points should be aligned while adding decimals.
Reason: Place values must remain in the correct columns.
Answer: A ✅
4.
Assertion: 100 hundredths make one whole.
Reason: Hundredths are equal parts of one unit.
Answer: A ✅
5.
Assertion: 8.2 is smaller than 8.15.
Reason: Compare tenths before hundredths.
Answer: C ✅
🧠 Brain Challenge
- Create three different decimal numbers between 4.5 and 4.6.
- Find two decimal numbers whose sum is exactly 15.
- Write a real-life example where decimal numbers are more useful than whole numbers.
- Can two different decimal numbers become equal by adding zeros to the end? Explain with an example.
- Create your own word problem involving decimal addition and solve it.
Case Study
Aarav visited a supermarket with his mother. They purchased the following items:
| Item |
Price (₹) |
| Notebook |
48.75 |
| Pen |
22.50 |
| Eraser |
8.25 |
| Scale |
15.50 |
Answer the Following Questions
- Find the total amount spent on all four items.
- Which item costs the least?
- How much more does the notebook cost than the pen?
- If Aarav pays ₹100, how much money will he receive back?
- Arrange all prices in ascending order.
Higher Order Thinking Skills (HOTS)
-
Write three different decimal numbers between
8.45 and 8.46.
-
Explain why
5.70 and
5.7 represent the same value.
-
Create a real-life situation where decimal subtraction is required.
-
A rope is 15.75 m long. It is cut into two unequal pieces.
Suggest two possible lengths.
-
Write any two decimal numbers whose sum is exactly
20.
Frequently Asked Questions
1. What is a decimal number?
A decimal number represents a whole number together with one or more parts of a whole.
2. Why do we use decimal numbers?
Decimals help us express measurements, money, weight and distance more accurately.
3. What is the first digit after the decimal point called?
It is called the tenths place.
4. Does adding zero after a decimal change its value?
No. For example,
4.5 = 4.50 = 4.500
5. What is the most common mistake while adding decimals?
Not aligning the decimal points properly.
Complete Chapter Summary
- We learned why smaller units are needed for accurate measurement.
- We understood decimal numbers and their place values.
- We represented decimals on the number line.
- We compared and ordered decimal numbers.
- We learned addition and subtraction of decimals.
- We solved practical questions involving money, length and weight.
- Regular practice helps improve speed and accuracy.
🏆 Final Challenge
Without using a calculator, solve the following:
- 18.75 + 9.35 − 4.60
- Arrange 7.08, 7.80, 7.18 and 7.008 in ascending order.
- Create your own shopping bill using at least five decimal prices and calculate the total.
🎉
Congratulations!
You have successfully completed
Class 7 Mathematics – Chapter 3: A Peek Beyond the Point.
You can now confidently:
- ✅ Read and write decimal numbers
- ✅ Understand place values
- ✅ Compare and order decimals
- ✅ Add and subtract decimal numbers
- ✅ Apply decimals in real-life situations
