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NCERT Solutions for Class 7 Maths Chapter 3 – A Peek Beyond the Point (Decimals)

The NCERT Solutions for Class 7 Maths Chapter 3 – A Peek Beyond the Point help students understand the concept of decimals, their representation, and practical usage in everyday measurements. These Ganita Prakash NCERT Class 7 Maths Solutions are prepared according to the latest CBSE and National Council of Educational Research and Training (NCERT) syllabus to improve students’ problem-solving skills and prepare them for exams like NTSE, JEE, and Olympiads. Download the free NCERT Class 7 Maths Chapter 3 PDF to practice and revise all questions.

NCERT Solutions for Class 7 Maths Chapter 3

This chapter introduces students to decimal numbers and how they are used in various real-life situations, including measurement of length, weight, and money. Understanding decimals lays the foundation for further studies in algebra, geometry, and data handling. The chapter focuses on smaller units, tenths, hundredths, and conversions between metric units.

Table of Contents

Key Concepts Covered in Chapter 3

Chapter 3 focuses on the use of decimals in measurement and arithmetic operations. It includes:

  • The need for smaller units – understanding tenths, hundredths, and thousandths.
  • Place value system for decimal numbers.
  • Conversion between units of length, weight, and money.
  • Comparison and ordering of decimal numbers.
  • Performing addition and subtraction using decimals.

Important Topics Explained

1. The Need for Smaller Units

Decimals are introduced to express quantities smaller than one unit. For example, 1 metre can be divided into 10 equal parts called decimetres. The need for smaller units arises when measurements such as screw lengths, pencil sizes, or distances cannot be expressed as whole numbers.

\(1 \text{ metre} = 10 \text{ decimetres} = 100 \text{ centimetres}\)

2. Understanding Tenths and Hundredths

Decimal numbers represent fractions in a simpler form. For example, \( \frac{1}{10} = 0.1 \) and \( \frac{1}{100} = 0.01 \). The concept of tenths and hundredths is introduced to measure precise quantities like 2.4 cm or 5.67 m.

\( \frac{3}{10} = 0.3, \quad \frac{25}{100} = 0.25 \)

3. Decimal Place Value System

The place value chart is expanded to the right of the ones place for decimal fractions. Every step to the right is one-tenth of the previous step.

PlaceValue
Tens10
Ones1
Tenths1/10 = 0.1
Hundredths1/100 = 0.01
Thousandths1/1000 = 0.001

4. Converting Units Using Decimals

Decimals are used to convert measurements of length, weight, and money efficiently. Conversion tables help understand metric relationships easily.

MeasurementConversion
1 m= 100 cm = 1000 mm
1 kg= 1000 g
1 Rupee= 100 Paise

5. Comparing Decimal Numbers

To compare decimal numbers, equalize the number of digits after the decimal point by adding zeros and then compare as whole numbers. Example: 3.45 < 3.50 since 45 < 50.

6. Operations on Decimals

Addition and subtraction of decimals follow the same rules as whole numbers, with the decimal point aligned vertically.

\( 25.936 + 8.202 = 34.138 \)

7. Visualising Decimals on a Number Line

Decimals can be represented between two whole numbers on a number line. For example, 0.5 lies midway between 0 and 1. Each division represents a tenth.

8. Application in Real Life

Decimals are applied in money transactions, weights, and measurements. For example, ₹2.50 means 2 rupees and 50 paise, and 1.75 m represents 1 metre and 75 centimetres.

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

Students can download the official NCERT PDF for Class 7 Maths Chapter 3 from the official NCERT and NCERTBooks.net websites. It includes all exercises and in-text examples.

Book TitleOfficial Download Link
Class 7 Mathematics – Chapter 3 A Peek Beyond the PointDownload PDF

Frequently Asked Questions on A Peek Beyond the Point

A decimal number is a way to represent fractions and smaller units using a point (.). For example, 0.25 represents 25 hundredths.

Decimals help in expressing precise quantities in measurement, currency, and daily calculations, improving numerical accuracy.

You can download the official PDF from NCERTBooks.net Class 7 Maths or from the official NCERT website.

Tenths represent one part of ten equal parts (0.1), and hundredths represent one part of hundred equal parts (0.01).

All NCERT Class 7 Maths solutions are available on NCERTBooks.net with detailed step-by-step answers.