What are decimal numbers, as explained in NCERT Class 7 Maths Chapter 3?

Decimal numbers are a way of representing numbers that include whole parts and fractional parts, where the fractional parts are powers of ten (tenths, hundredths, thousandths, etc.). They are separated by a decimal point.

How do you add and subtract decimal numbers according to this chapter?

To add or subtract decimal numbers, you must align the decimal points vertically, ensuring that digits of the same place value are in the same column. Then, you perform addition or subtraction as you would with whole numbers, carrying over or borrowing as needed.

What is the significance of "tenths" and "hundredths" in this chapter?

"Tenths" (1/10) and "hundredths" (1/100) are fundamental fractional units introduced to represent values smaller than one whole. Understanding these units is crucial for grasping the place value system of decimals and accurately performing measurements and calculations involving parts of a whole.

How do you compare decimal numbers?

To compare decimal numbers, first compare their whole number parts. If they are the same, move to the tenths place and compare the digits. If those are also the same, move to the hundredths place, and so on, until you find a difference. Adding zeros to the right of the last non-zero digit after the decimal point does not change the value of the number and can help in comparison (e.g., 0.5 is equivalent to 0.50).

Are conversions between units (like cm to m, or g to kg) covered using decimals in this chapter?

Yes, the chapter uses practical examples involving measurements (like length and weight) to demonstrate how decimals are used to express quantities in different units. For instance, converting centimetres to metres or grams to kilograms involves applying decimal understanding.

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NCERT Solutions

Class 7

Maths

Chapter 3 A Peek Beyond the Point

NCERT Solutions Class 7 Maths Chapter 3 A Peek Beyond the Point

NCERT Solutions Class 7 Maths Chapter 3 A Peek Beyond the Point introduces students to decimal numbers in a fun and easy way. In this NCERT Solutions Class 7 Maths Chapter, students learn how to read, write, and use decimals in daily life—like when dealing with money, length, or weight. It also covers how to compare, add, and subtract decimal numbers step by step.

These NCERT Solutions are designed to help students clearly understand each concept through simple language and solved examples. With detailed explanations and practice problems, students can gain confidence and improve their calculation skills

1.0NCERT Solutions Class 7 Maths Chapter 3 A Peek Beyond the Point – Download PDF

Get your FREE PDF of NCERT Solutions Class 7 Maths Chapter 3 – A Peek Beyond the Point, created by the subject experts at ALLEN.

NCERT Solutions for Class 7 Maths Chapter 3: A Peek Beyond the Point

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2.0Key Concepts in Chapter 3: A Peek Beyond the Point

1. Understanding Decimal Numbers

Decimals represent numbers that lie between whole numbers.

They are used when precision is required, such as measuring length (5.6 cm), weight (3.75 kg), or money (₹45.50).

Decimal numbers are expressed with digits to the right of the decimal point, representing parts of a whole.

2. Reading and Writing Decimals

Students learn how to read and write decimal numbers up to hundredths and thousandths.

Example: 3.07 is read as “three point zero seven”.

3. Place Value System (Decimal Version)

The place values to the right of the decimal point include:

Tenths (1/10)
Hundredths (1/100)
Thousands (1/1000)
Example: In 4.236 → 2 is tenths, 3 is hundredths, and 6 is thousandths.

4. Comparing Decimal Numbers

Students learn to compare decimal values based on place values.

Extra zeroes do not affect the value: 3.6 = 3.60

Example: 3.45 > 3.4 because 3.45 has 5 hundredths vs. 0.

5. Conversion between Fractions and Decimals

Converting decimals to fractions and vice versa strengthens understanding of their relationship.

Example: 0.25 = 25/100 = 1/4

6. Operations on Decimals

a) Addition and Subtraction

Align decimal points to perform operations correctly.

Ensure place values are matched while adding or subtracting.

b) Multiplication

Multiply as if they are whole numbers.

Place the decimal point in the result based on total decimal places in the multiplicands.

Example: 1.2 × 3.4 = 4.08

c) Division

Adjust the divisor or dividend by shifting the decimal point to make division easier.

Example: 2.5 ÷ 0.5 = 5

7. Use of Decimals in Daily Life

Understanding decimals is important for:

Money transactions (e.g., ₹129.75)
Measurement units (cm, kg, litre)
Data interpretation (statistics, averages, percentages)

3.0Key Features of NCERT Solutions Class 7 Maths Chapter 3 : A Peek Beyond the Point

Concept-Oriented Explanations: Every fundamental concept, from the definition of tenths to complex decimal operations, is explained with clear and precise language, making it easy for students to grasp even challenging ideas.
Step-by-Step Problem Solving: Solutions to all textbook exercises are provided with detailed, step-by-step working. This methodical approach helps students understand the logic and process behind each answer, fostering independent problem-solving skills.
Real-Life Examples: The solutions connect decimal concepts to practical scenarios, like measuring lengths or converting units, reinforcing the real-world relevance and application of decimals.
Adherence to NCERT Syllabus: Meticulously aligned with the latest NCERT curriculum (Ganita Prakash), our solutions ensure that students are studying the most current and relevant content for their examinations.
Focus on Place Value: A strong emphasis is placed on understanding decimal place values, which is fundamental to performing all operations correctly and comparing decimals accurately.
Downloadable PDF: Available in a convenient PDF format, enabling students to study offline, anytime, and anywhere, ensuring uninterrupted learning.