Mathematics chapters3 of 15

Class 7MathematicsChapter 3NCERT • Ganita Prakash

A Peek Beyond the Point

Understand numbers smaller than one using tenths, hundredths and thousandths, and learn to work confidently with decimals.

Chapter Snapshot

Decimals help us represent quantities smaller than one whole unit.
Tenths come from dividing one unit into 10 equal parts.
Hundredths come from dividing one unit into 100 equal parts.
Thousandths come from dividing one unit into 1000 equal parts.
Decimal place value extends to the right of the decimal point.
Decimals are useful in length, mass and money.
Decimals can be compared using place value.
Decimal addition and subtraction work like whole numbers when place values are aligned.

What You Will Learn

Understand tenths, hundredths and thousandths
Write fractions as decimals
Read decimal numbers correctly
Understand decimal place value
Convert common measurement units
Locate decimals on a number line
Compare decimal numbers
Add and subtract decimals

Exam PriorityBoardsVery HighFoundationHigh

Chapter Overview

Whole numbers are not always enough for accurate measurement.

Suppose an object is longer than 2 cm but shorter than 3 cm. Writing only 2 cm or 3 cm would not describe its exact length.

For such situations, we divide a whole unit into smaller equal parts.

This leads us to tenths, hundredths, thousandths and decimal numbers.

1. The Need for Smaller Units

Measurements often fall between two whole numbers.

For example:

2\frac{7}{10} = 2.7

So decimals help us write parts of a whole in a shorter form.

2. Tenths

Divide one whole into 10 equal parts.

Each part is one tenth.

Examples:

\frac{7}{10} = 0.7

3\frac{4}{10} = 3.4

Quick Check

Write 6/10 in decimal form.

Show answer

0.6

3. Hundredths

Divide one whole into 100 equal parts.

Each part is one hundredth.

For example:

\frac{35}{100} = 0.35

Writing Hundredths as a Decimal

Question

Write 2 ones, 3 tenths and 5 hundredths in decimal form.

Solution

2 + \frac{3}{10} + \frac{5}{100}

4. Thousandths

Divide one whole into 1000 equal parts.

Each part is one thousandth.

For example, 3.247 means:

3 ones
2 tenths
4 hundredths
7 thousandths

Decimal Places

Place	Fraction	Decimal Value
Ones	1	1
Tenths	1/10	0.1
Hundredths	1/100	0.01
Thousandths	1/1000	0.001

5. Decimal Place Value

Consider:

245.378

It means:

2 hundreds
4 tens
5 ones
3 tenths
7 hundredths
8 thousandths

Expanded Form

245.378 = 200 + 40 + 5 + \frac{3}{10} + \frac{7}{100} + \frac{8}{1000}

Decimal Place Value

Question

Write 4 ones and 6 hundredths in decimal form.

Solution

4 + 0.06 = \boxed{4.06}

6. Equivalent Decimals

Adding zeroes at the end of a decimal does not change its value.

4.5 = 4.50 = 4.500

But:

4.5 \ne 4.05

7. Decimals in Measurement

Length

1\text{ m} = 100\text{ cm}

1\text{ cm} = 10\text{ mm}

1\text{ m} = 1000\text{ mm}

Mass

1\text{ kg} = 1000\text{ g}

Money

1\text{ rupee} = 100\text{ paise}

Therefore:

50\text{ paise} = \text{Rs. }0.50

Rupees and Paise

Question

Write ₹8 and 75 paise in decimal form.

Solution

75\text{ paise} = \text{Rs. }0.75

8. Decimals on a Number Line

To locate 1.4, divide the interval from 1 to 2 into 10 equal parts.

The fourth mark after 1 represents 1.4.

To locate 1.45, divide the interval between 1.4 and 1.5 into 10 equal parts.

9. Comparing Decimals

Compare decimals using place value.

Example:

0.2 > 0.02 > 0.002

Compare Decimals

Question

Which is greater: 3.45 or 3.405?

Solution

3.45 = 3.450

10. Addition of Decimals

The key rule is:

Align the decimal points.

Adding Decimals

Question

Find 2.7 + 3.5.

Solution

2.7 + 3.5 = 6.2

11. Subtraction of Decimals

Again, align the decimal points.

Subtracting Decimals

Question

Find 3.5 - 2.7.

Solution

3.50 - 2.70 = 0.80

Important Terms

Key Terms

DecimalDecimal PointTenthsHundredthsThousandthsDecimal Place ValueEquivalent DecimalsNumber Line

Exam Focus

Important Exam Topics

tenths, hundredths and thousandths;
fraction to decimal conversion;
decimal place value;
expanded form;
equivalent decimals;
unit conversions;
number-line representation;
comparing decimals;
addition and subtraction of decimals.

Quick Revision

$\frac{1}{10}=0.1$
$\frac{1}{100}=0.01$
$\frac{1}{1000}=0.001$
10 tenths make 1 whole.
10 hundredths make 1 tenth.
10 thousandths make 1 hundredth.
$4.5 = 4.50 = 4.500$ .
Compare decimals using place value.
Align decimal points when adding or subtracting.

Practice Questions

Q1MCQEasyClass 7

\frac{7}{10}

View Solution

Answer: B. 0.7

Q2MCQEasyClass 7

Which is the greatest? A. 0.5 B. 0.05 C. 0.005 D. 0.0005

View Solution

Answer: A. 0.5

Q3Short AnswerModerateClass 7

0.7,\quad 0.07,\quad 0.77,\quad 0.707

View Solution

0.070 < 0.700 < 0.707 < 0.770

Q4NumericalEasyClass 7

5.3 + 2.6

View Solution

5.3 + 2.6 = \boxed{7.9}

Q5NumericalModerateClass 7

10.4 - 4.5

View Solution

10.4 - 4.5 = \boxed{5.9}

Q6NumericalModerateFoundation

A ribbon is 3.5 m long. Another ribbon is 2.75 m long. Find their total length.

View Solution

3.50 + 2.75 = 6.25

Apply Your Learning

Decimals Around You

Find three examples of decimals around you.

You may look at:

prices;
rulers;
weighing scales;
distances.

For each number:

read it aloud;
identify its decimal places;
write its expanded form;
compare it with another decimal.

Chapter Summary

Decimals represent parts smaller than one whole.
One tenth is 0.1.
One hundredth is 0.01.
One thousandth is 0.001.
Place value continues to the right of the decimal point.
Trailing zeroes do not change a decimal's value.
Decimals are useful in measurement and money.
Compare decimals using place value.
Align decimal points when adding and subtracting decimals.

Mathematics chapters3 of 15

Class 7MathematicsChapter 3NCERT • Ganita Prakash

A Peek Beyond the Point

Understand numbers smaller than one using tenths, hundredths and thousandths, and learn to work confidently with decimals.

Chapter Snapshot

Decimals help us represent quantities smaller than one whole unit.
Tenths come from dividing one unit into 10 equal parts.
Hundredths come from dividing one unit into 100 equal parts.
Thousandths come from dividing one unit into 1000 equal parts.
Decimal place value extends to the right of the decimal point.
Decimals are useful in length, mass and money.
Decimals can be compared using place value.
Decimal addition and subtraction work like whole numbers when place values are aligned.

What You Will Learn

Understand tenths, hundredths and thousandths
Write fractions as decimals
Read decimal numbers correctly
Understand decimal place value
Convert common measurement units
Locate decimals on a number line
Compare decimal numbers
Add and subtract decimals

Exam PriorityBoardsVery HighFoundationHigh

Chapter Overview

Whole numbers are not always enough for accurate measurement.

Suppose an object is longer than 2 cm but shorter than 3 cm. Writing only 2 cm or 3 cm would not describe its exact length.

For such situations, we divide a whole unit into smaller equal parts.

This leads us to tenths, hundredths, thousandths and decimal numbers.

1. The Need for Smaller Units

Measurements often fall between two whole numbers.

For example:

2\frac{7}{10} = 2.7

So decimals help us write parts of a whole in a shorter form.

2. Tenths

Divide one whole into 10 equal parts.

Each part is one tenth.

Examples:

\frac{7}{10} = 0.7

3\frac{4}{10} = 3.4

Quick Check

Write 6/10 in decimal form.

Show answer

0.6

3. Hundredths

Divide one whole into 100 equal parts.

Each part is one hundredth.

For example:

\frac{35}{100} = 0.35

Writing Hundredths as a Decimal

Question

Write 2 ones, 3 tenths and 5 hundredths in decimal form.

Solution

2 + \frac{3}{10} + \frac{5}{100}

4. Thousandths

Divide one whole into 1000 equal parts.

Each part is one thousandth.

For example, 3.247 means:

3 ones
2 tenths
4 hundredths
7 thousandths

Decimal Places

Place	Fraction	Decimal Value
Ones	1	1
Tenths	1/10	0.1
Hundredths	1/100	0.01
Thousandths	1/1000	0.001

5. Decimal Place Value

Consider:

245.378

It means:

2 hundreds
4 tens
5 ones
3 tenths
7 hundredths
8 thousandths

Expanded Form

245.378 = 200 + 40 + 5 + \frac{3}{10} + \frac{7}{100} + \frac{8}{1000}

Decimal Place Value

Question

Write 4 ones and 6 hundredths in decimal form.

Solution

4 + 0.06 = \boxed{4.06}

6. Equivalent Decimals

Adding zeroes at the end of a decimal does not change its value.

4.5 = 4.50 = 4.500

But:

4.5 \ne 4.05

7. Decimals in Measurement

Length

1\text{ m} = 100\text{ cm}

1\text{ cm} = 10\text{ mm}

1\text{ m} = 1000\text{ mm}

Mass

1\text{ kg} = 1000\text{ g}

Money

1\text{ rupee} = 100\text{ paise}

Therefore:

50\text{ paise} = \text{Rs. }0.50

Rupees and Paise

Question

Write ₹8 and 75 paise in decimal form.

Solution

75\text{ paise} = \text{Rs. }0.75

8. Decimals on a Number Line

To locate 1.4, divide the interval from 1 to 2 into 10 equal parts.

The fourth mark after 1 represents 1.4.

To locate 1.45, divide the interval between 1.4 and 1.5 into 10 equal parts.

9. Comparing Decimals

Compare decimals using place value.

Example:

0.2 > 0.02 > 0.002

Compare Decimals

Question

Which is greater: 3.45 or 3.405?

Solution

3.45 = 3.450

10. Addition of Decimals

The key rule is:

Align the decimal points.

Adding Decimals

Question

Find 2.7 + 3.5.

Solution

2.7 + 3.5 = 6.2

11. Subtraction of Decimals

Again, align the decimal points.

Subtracting Decimals

Question

Find 3.5 - 2.7.

Solution

3.50 - 2.70 = 0.80

Important Terms

Key Terms

DecimalDecimal PointTenthsHundredthsThousandthsDecimal Place ValueEquivalent DecimalsNumber Line

Exam Focus

Important Exam Topics

tenths, hundredths and thousandths;
fraction to decimal conversion;
decimal place value;
expanded form;
equivalent decimals;
unit conversions;
number-line representation;
comparing decimals;
addition and subtraction of decimals.

Quick Revision

$\frac{1}{10}=0.1$
$\frac{1}{100}=0.01$
$\frac{1}{1000}=0.001$
10 tenths make 1 whole.
10 hundredths make 1 tenth.
10 thousandths make 1 hundredth.
$4.5 = 4.50 = 4.500$ .
Compare decimals using place value.
Align decimal points when adding or subtracting.

Practice Questions

Q1MCQEasyClass 7

\frac{7}{10}

View Solution

Answer: B. 0.7

Q2MCQEasyClass 7

Which is the greatest? A. 0.5 B. 0.05 C. 0.005 D. 0.0005

View Solution

Answer: A. 0.5

Q3Short AnswerModerateClass 7

0.7,\quad 0.07,\quad 0.77,\quad 0.707

View Solution

0.070 < 0.700 < 0.707 < 0.770

Q4NumericalEasyClass 7

5.3 + 2.6

View Solution

5.3 + 2.6 = \boxed{7.9}

Q5NumericalModerateClass 7

10.4 - 4.5

View Solution

10.4 - 4.5 = \boxed{5.9}

Q6NumericalModerateFoundation

A ribbon is 3.5 m long. Another ribbon is 2.75 m long. Find their total length.

View Solution

3.50 + 2.75 = 6.25

Apply Your Learning

Decimals Around You

Find three examples of decimals around you.

You may look at:

prices;
rulers;
weighing scales;
distances.

For each number:

read it aloud;
identify its decimal places;
write its expanded form;
compare it with another decimal.

Chapter Summary

Decimals represent parts smaller than one whole.
One tenth is 0.1.
One hundredth is 0.01.
One thousandth is 0.001.
Place value continues to the right of the decimal point.
Trailing zeroes do not change a decimal's value.
Decimals are useful in measurement and money.
Compare decimals using place value.
Align decimal points when adding and subtracting decimals.