In Class 7 Maths Chapter 3 A Peek Beyond the Point, students take an important step forward in their understanding of numbers by exploring decimals, place value beyond the decimal point, and operations on decimals.
The chapter helps students understand how numbers smaller than one are represented and used in real life – whether measuring length in millimetres, weighing items in grams, or recording precise quantities in science experiments. In A Peek Beyond the Point, students learn:
- The need for smaller units (tenths, hundredths, thousandths)
- Decimal place value system
- Writing and reading decimal numbers
- Locating decimals on a number line
- Comparing decimal numbers
- Addition and subtraction of decimals
- Converting units (mm–cm–m, g–kg, rupee–paise)
- Solving real-life word problems using decimals
A Peek Beyond the Point Worksheet
The Class 7 Maths Worksheet Chapter 3 A Peek Beyond the Point contains a wide variety of carefully designed questions that cover all concepts of decimals as per the NCERT syllabus.
Understanding decimals clearly ensures students avoid common mistakes in addition, subtraction, comparison, and unit conversion. This worksheet helps students build strong conceptual understanding and improve calculation accuracy through structured practice.
Designed as per the latest school-level assessment pattern, these paper helps practicing:
- Addition, subtraction and comparison of decimals
- Understanding tenths, hundredths, and thousandths
- Unit conversion
- Real-life application problems
- Expanded and standard form
Download the printable PDF and boost your preparation with structured practice and detailed solutions. Also check other chapter of Maths Class 7 here.
Chapter 3 : A Peek Beyond the Point Notes
Have you ever noticed how small differences in measurements matter? A slightly longer screw, a slightly heavier packet, or a slightly longer cloth piece can change everything!
This chapter begins with a simple situation — measuring screws — and gradually introduces an important mathematical idea.
The Need for Smaller Units
Sometimes whole numbers are not enough to measure accurately.
A unit can be divided into 10 equal parts → each part is 1/10 (one-tenth).
Example:
2 7/10 cm means:
2 cm + 7 tenths of a cm.
Why divide into smaller units?
Because:
- Exact measurement is needed.
- Small differences matter in real life.
Tenth Part
If one unit is divided into 10 equal parts:
1 unit=10 tenths
Example: 3 4/10 = 3 + 4/10
Also: 34/10=3 4/10
Addition of Tenths
Example:
2 7/10 + 3 6/10
Add units and tenths separately:
Units: 2 + 3 = 5
Tenths: 7/10 + 6/10 = 13/10
Since 10/10 = 1,
5 + 13/10 = 6 3/10
Subtraction of Tenths
If tenths are insufficient, borrow 1 unit:
Example:
12 4/10 – 6 7/10
Convert:
12 = 11 + 10/10
Now subtract.
A Hundredth Part
If 1 unit is divided into 100 equal parts:
1 hundredth = 1/100
Decimal Notation
Instead of writing:
4 5/10
We write: 4.5
Decimal point separates whole number and fractional part.
Writing and Reading Decimals
70.5 → seventy point five
7.05 → seven point zero five
0.274 → zero point two seven four
Trailing zeros do not change value:
0.2 = 0.20 = 0.200
But:
0.2 ≠ 0.02
Locating Decimals on Number Line
- 1.4 lies between 1 and 2.
- Divide the segment into 10 equal parts.
- Take the 4th division.
Comparing Decimals
Compare place values:
Example:
6.456 and 6.465
Units same → Tenths same → Compare hundredths
5 < 6
So,
6.465 is greater.
Closest Decimal
To find closest to 1:
Compare difference from 1.
Example:
1.01 is closer than 0.9 because:
1.01 – 1 = 0.01
1 – 0.9 = 0.1
Unit Conversions
Length
1 cm = 10 mm
1 mm = 0.1 cm
1 m = 100 cm
1 cm = 0.01 m
Weight
1 kg = 1000 g
1 g = 0.001 kg
Money
1 rupee = 100 paise
1 paisa = 0.01 rupee
75 paise = ₹0.75