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Mathematics Class 6 - Decimals Notes

Comprehensive study notes for Class 6 - Decimals olympiad preparation

Decimals

Welcome to the chapter on Decimals for Class 6. In this chapter, you will learn what decimals are, how to read and write them, how to compare and order decimals, and how to perform operations with decimals. By the end of this chapter, you will be able to use decimals in real-life situations and solve problems confidently!

Introduction

Decimals are numbers that have a whole part and a fractional part, separated by a dot called the decimal point. Decimals are used in money, measurements, and many other places.

What is a Decimal?

A decimal number has two parts:

  • Whole part: The part before the decimal point.
  • Decimal part: The part after the decimal point.

Example: In 12.45, 12 is the whole part and 45 is the decimal part.

Reading and Writing Decimals

  • 0.5 is read as "zero point five"
  • 3.75 is read as "three point seven five"
  • 10.08 is read as "ten point zero eight"

Place Value in Decimals

The place value after the decimal point is:

  • First place: tenths (0.1, 0.2, ...)
  • Second place: hundredths (0.01, 0.02, ...)
  • Third place: thousandths (0.001, 0.002, ...)

Example: In 4.326, 3 is tenths, 2 is hundredths, 6 is thousandths.

Comparing and Ordering Decimals

  • Compare the whole part first.
  • If the whole part is same, compare the decimal part digit by digit.
  • Example: 2.45 < 2.56 because 45 < 56

Operations with Decimals

You can add, subtract, multiply, and divide decimals just like whole numbers, but keep the decimal point in the correct place.

  • Addition: Line up the decimal points and add.
  • Subtraction: Line up the decimal points and subtract.
  • Multiplication: Multiply as whole numbers, then count and place the decimal point.
  • Division: Move the decimal point as needed and divide.

Example: 2.5 + 1.75 = 4.25
5.6 - 2.3 = 3.3
0.4 × 2 = 0.8
4.8 ÷ 2 = 2.4

Decimals in Daily Life

  • Money: ₹12.50 means twelve rupees and fifty paise.
  • Length: 1.75 meters
  • Weight: 2.5 kilograms

Fun Activity: Decimal Hunt!

Look for decimals around you—on price tags, measuring tapes, or clocks. Write down five examples!

Summary

  • Decimals have a whole part and a decimal part.
  • Place value is important in decimals.
  • You can compare, add, subtract, multiply, and divide decimals.
  • Decimals are used in money, measurement, and daily life.

Practice Questions

  1. Write 0.75 in words.
  2. Which is greater: 3.25 or 3.52?
  3. Add: 1.5 + 2.25
  4. Subtract: 5.6 - 2.4
  5. Multiply: 0.3 × 5
  6. Divide: 4.8 ÷ 2

Challenge Yourself

  • Write three examples of decimals used in daily life.
  • Arrange these decimals in order: 2.5, 2.05, 2.55, 2.15

Did You Know?

  • Decimals are another way to write fractions!
  • 0.5 is the same as 1/2, and 0.25 is the same as 1/4.

Glossary

  • Decimal: A number with a whole part and a fractional part separated by a decimal point.
  • Decimal Point: The dot that separates the whole part from the decimal part.
  • Tenths: The first place after the decimal point.
  • Hundredths: The second place after the decimal point.

Answers to Practice Questions

  1. Zero point seven five
  2. 3.52
  3. 3.75
  4. 3.2
  5. 1.5
  6. 2.4

Practice working with decimals to become confident in math!

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