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CBSE • Class 6 • Mathematics • Ch 8

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Decimals

In CBSE Class 6 Mathematics, "Decimals" explores decimal place value representation: tenths (1/10), hundredths (1/100), and thousandths (1/1000). Students learn to read, write, and compare decimals, convert fractions into decimals and vice versa, apply decimals in currency (rupees/paise), length (km/m/cm/mm), and weight (kg/g), and perform addition and subtraction of decimals aligning decimal points.

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🪙 Have You Ever Wondered?

Why is 75 paise written as ₹0.75, and how is 0.5 completely different from 0.05?

Decimals are the base-10 extension of our place value system to fractions with denominators 10, 100, and 1000! Discover how decimals power world currencies and precision measurement.

Why This Chapter Matters

Before You Begin (Prerequisites)

Fractions concept
Indian place value system (Ones, Tens, Hundreds)

What You Will Learn (Core Objectives)

Understand tenths, hundredths, and thousandths place values.
Convert fractions with denominators 10, 100, 1000 into decimals and vice versa.
Compare decimals by comparing whole parts, then tenths, then hundredths.
Apply decimals in money (Rs and paise), length (m and cm), and weight (kg and g).
Add and subtract decimals by vertically aligning the decimal points.

Chapter Roadmap & Progression

1 1. Tenths, Hundredths & Thousandths...

2 2. Conversion & Practical Applicati...

3 3. Addition and Subtraction of Deci...

Complete Concept Guide (100% Curriculum Coverage)

1. Tenths, Hundredths & Thousandths Place Value

The dot between whole number and fractional parts is the decimal point.

Hundreds (100)	Tens (10)	Ones (1)	.	Tenths (1/10)	Hundredths (1/100)	Thousandths (1/1000)
2	4	5	.	8	7	3

$245.873 = 200 + 40 + 5 + \frac{8}{10} + \frac{7}{100} + \frac{3}{1000}$.

2. Conversion & Practical Applications

Money: $100\text{ paise} = ₹1 \implies 1\text{ paisa} = ₹\frac{1}{100} = ₹0.01$. Thus, $65\text{ paise} = ₹0.65$.
Length: $1\text{ m} = 100\text{ cm} \implies 1\text{ cm} = 0.01\text{ m}$. $1\text{ km} = 1000\text{ m} \implies 1\text{ m} = 0.001\text{ km}$.
Weight: $1\text{ kg} = 1000\text{ g} \implies 1\text{ g} = 0.001\text{ kg}$.

3. Addition and Subtraction of Decimals

To add or subtract decimals:

Convert unlike decimals into like decimals by appending trailing zeros (e.g. $4.5 = 4.50$).
Write the numbers vertically so that the decimal points are aligned in a straight column.
Add or subtract as whole numbers, placing the decimal point in the answer directly below the column of decimal points.

Key Formulas, Identities & Theorems

Decimal Fraction Definition

$$0.1 = \frac{1}{10}, \quad 0.01 = \frac{1}{100}, \quad 0.001 = \frac{1}{1000}$$

Base-10 fractional expansion.

Conceptual Solved Examples & Case Studies

Example 1

Express 2 m 45 cm in metres using decimals.

Step-by-Step Solution:

$45\text{ cm} = \frac{45}{100}\text{ m} = 0.45\text{ m}$.
Total $= 2\text{ m} + 0.45\text{ m} = \mathbf{2.45\text{ m}}$.

Example 2

Find the value of: 27.076 + 0.55 + 0.004.

Step-by-Step Solution:

Align decimal points vertically:
$\begin{array}{r@{\quad}l} & 27.076 \\ + & \phantom{0}0.550 \\ + & \phantom{0}0.004 \\ \hline & \mathbf{27.630} \end{array}$

Common Misconceptions & Examiner Traps

Common Misconception

Aligning decimal numbers by rightmost digits instead of decimal points.

Scientific Reality & Correction

Always align decimal points vertically! Adding 12.3 and 1.45 by right digits gives an incorrect place value calculation.

Visual Learning & Conceptual Map

Decimal Unit Conversions

Standard Metric Relationships

Currency

1 paisa = ₹0.01
75 p = ₹0.75

Length

1 cm = 0.01 m
1 m = 0.001 km

Mass

1 g = 0.001 kg
450 g = 0.450 kg

Chapter Summary & 10 Key Takeaways

Takeaway 1

Decimals represent tenths, hundredths, thousandths.

Takeaway 2

Decimal point separates whole number and fractional parts.

Takeaway 3

Convert metric units and currency using division by 10, 100, 1000.

Takeaway 4

Align decimal points in a straight vertical column during addition/subtraction.

Check Your Understanding (Diagnostic Practice Questions)

Diagnostic questions testing core conceptual clarity. Answers are hidden initially — solve each problem first, then click to reveal the step-by-step verified solution.

Subtract 2.051 from 5.4.

Reveal Answer & Explanation

Answer: Convert to like decimals: $5.400 - 2.051 = \mathbf{3.349}$.
Add trailing zeros to 5.4.

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