Master Chapter 3 Class 7 - A peek beyond the Point (Ganita Prakash) with comprehensive NCERT Solutions, Practice Questions, MCQs, Sample Papers, Case Based Questions, and Video lessons.
Start Learning NowWelcome to Chapter 3, A Peek Beyond the Point, from your Class 7 Maths book, Ganita Prakash.
This chapter introduces one of the most important and useful concepts in all of mathematics: decimal numbers.
We start by asking a simple question: how do you measure something precisely? Imagine trying to measure a small screw. Your ruler might tell you it's "between 2 cm and 3 cm," but that isn't very accurate. To solve this, we need to use units smaller than 1.
This chapter builds the idea of decimals from the ground up, starting with fractions and connecting them to our place value system.
The Need for Smaller Units (Tenths)
First, we will see how we can get more precise by dividing one whole unit (like 1 cm) into 10 equal parts. Each of these new, smaller parts is called a tenth (1/10). This allows us to measure our screw much more accurately, for example, as 2 7/10 cm.
Even Smaller Units (Hundredths)
But what if we need to be even more precise? The chapter shows how we can take each tenth and divide it into 10 smaller parts. This new, tiny unit is a hundredth (1/100). We will learn that 10 hundredths make 1 tenth, and 100 hundredths make 1 whole unit.
The Decimal Point and Place Value
The most important part of this chapter is why we use 10. It's because our entire number system (Ones, Tens, Hundreds) is already based on 10. Decimals are simply a way to extend this place value system to the right, to show parts smaller than 1.
The decimal point ('.') is the crucial separator.
To the left of the point are the whole numbers: Ones, Tens, Hundreds, etc.
To the right of the point are the fractional parts: Tenths, Hundredths, Thousandths, etc.
Decimals in the Real World (Units)
You will learn how to read, write, and use this new decimal notation in everyday life. We will see that this is the system we use for:
Money: 1 paisa is 1/100 of a rupee, which we write as ₹ 0.01.
Length: 1 mm is 1/10 of a cm (0.1 cm), and 1 cm is 1/100 of a meter (0.01 m).
Weight: 1 g is 1/10 of a kg (0.001 kg).
Comparing, Adding, and Subtracting Decimals
Finally, you will learn the rules for working with these numbers.
Comparing: How do you tell if 6.456 or 6.465 is bigger? You'll learn to compare them digit by digit, from left to right.
Operations: You will master how to add and subtract decimals, learning the most important rule: always line up the decimal points before you start.
Mastering decimals is an essential skill, necessary for everything from handling money to science and engineering. At Teachoo, we break down every concept—from place value tables to decimal addition—in a clear, step-by-step way to help you understand it perfectly.
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