Class 7 Maths Chapter 3 A Peek Beyond the Point | NCERT Ganita Prakash Complete Explanation & Solutions
Class 7 Maths Chapter 3 A Peek Beyond the Point | NCERT Ganita Prakash Complete Explanation & Solutions
Introduction
In many real-life situations we need more precise measurements than whole numbers.
Examples:
• Length of a wire
• Weight of vegetables
• Distance between two points
To measure such quantities, we use decimal numbers.
Examples:
2.5 m
3.75 kg
0.8 km
Decimals help represent parts of a whole number.
In this chapter students learn:
• Decimal place values
• Tenths and hundredths
• Comparing decimal numbers
• Decimal sequences
• Addition and subtraction of decimals
1. Decimal Place Value
A decimal number contains two parts:
Whole number part
Decimal part
Example
4.45
Here:
4 → units
4 → tenths
5 → hundredths
So we read it as:
Four units, four tenths, five hundredths.
Tenths and Hundredths
When one unit is divided into 10 equal parts, each part is called one-tenth.
1 tenth = 1/10 = 0.1
If each tenth is further divided into 10 parts, we get hundredths.
1 hundredth = 1/100 = 0.01
Thus
1 unit = 10 tenths = 100 hundredths.
Example
The length of a folded paper ends at:
4 units + 4 tenths + 5 hundredths
Decimal form:
4.45
2. Writing Decimals in Different Ways
1 unit + 1 tenth + 4 hundredths
1 + 0.1 + 0.04
Decimal form:
1.14
Another form:
114 / 100
These different forms represent the same number.
3. Comparing Decimal Numbers
To compare decimals:
Step 1: Compare whole numbers
Step 2: Compare tenths
Step 3: Compare hundredths
Example:
6.456 and 6.465
Both have:
6 units
4 tenths
Now compare hundredths
5 < 6
So
6.456 < 6.465
Example Questions
Which is greater?
1.23 or 1.32
Compare tenths:
2 < 3
Therefore
1.32 is greater
Which is greater?
1.009 or 1.090
Compare hundredths:
0 < 9
Therefore
1.090 > 1.009
4. Closest Decimal Numbers
0.9
1.01
1.1
1.11
We want the number closest to 1.
Distance from 1:
1.01 → 0.01 away
0.9 → 0.1 away
Since 0.01 is smaller,
1.01 is closest to 1.
5. Decimal Sequences
Example sequence:
4.4, 4.8, 5.2, 5.6, 6.0 …
Observe the pattern.
Each number increases by 0.4.
Next numbers:
6.4
6.8
7.2
6. Addition of Decimals
Example
Priya needs 2.7 m cloth.
Shylaja needs 3.5 m cloth.
Total cloth required:
2.7 + 3.5
Step 1
Add tenths
7 + 5 = 12 tenths
12 tenths = 1 unit + 2 tenths
Step 2
2 + 3 + 1 = 6
Final answer:
6.2 m
7. Subtraction of Decimals
Example
3.5 – 2.7
Step 1
Borrow from units.
3.5 = 2 units + 15 tenths
Step 2
15 − 7 = 8
Answer:
0.8
Example from NCERT
Find:
15.34 + 2.68
Step 1
15.34
2.68
Step 2
4 + 8 = 12
Write 2, carry 1
Step 3
3 + 6 + 1 = 10
Write 0, carry 1
Step 4
5 + 2 + 1 = 8
Answer:
18.02
Figure It Out – Important Solutions
Question 1: Find the Sums
a) 5.3 + 2.6
= 7.9
b) 18 + 8.8
= 26.8
c) 2.15 + 5.26
= 7.41
d) 9.01 + 9.10
= 18.11
e) 29.19 + 9.91
= 39.10
f) 0.934 + 0.6
= 1.534
g) 0.75 + 0.03
= 0.78
h) 6.236 + 0.487
= 6.723
Question 2: Find the Differences
a) 5.6 − 2.3
= 3.3
b) 18 − 8.8
= 9.2
c) 10.4 − 4.5
= 5.9
d) 17 − 16.198
= 0.802
e) 17 − 0.05
= 16.95
f) 34.505 − 18.1
= 16.405
g) 9.9 − 9.09
= 0.81
h) 6.236 − 0.487
= 5.749
Key Concepts from This Chapter
Students learned:
• Decimal place value system
• Tenths and hundredths
• Comparing decimals
• Decimal sequences
• Addition of decimals
• Subtraction of decimals
These concepts help students perform accurate measurements and calculations in daily life.
Practice Challenge
Try these questions.
Arrange in ascending order:
2.45, 2.54, 2.405
Find the sum:
7.25 + 3.86
Find the difference:
9.75 − 4.38
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