Notes Maths Class 7 Chapter 3 Ganita Prakash

Notes For All Chapters – Ganita Prakash Class 7th

A Peek Beyond the Point

1. Need for Smaller Units

Even a tiny difference in length (like in screws) matters in measurements.

To measure small lengths accurately, we divide 1 cm into 10 parts, each called 1 tenth (1/10) of a cm.

2. Understanding Tenths

1 unit = 10 tenths

Example: 2\(\frac{7}{10}\) = 2+\(\frac{7}{10}\) =2.7

Reading decimals:

• 3.4 = Three and four-tenths
• 4.1 = Four and one-tenth

3. Adding and Subtracting Tenths

To add: 2.7 + 3.6 = 6.3

To subtract: 3.5 − 2.7 = 0.8

4. Understanding Hundredths

• 1 tenth = 10 hundredths
• 1 unit = 100 hundredths

Example:

4\(\frac{45}{100}\) = 4.45

5. Decimal Place Value System

Decimal Point (.) separates whole and fractional parts.

Example:

• 70.5 = 70 + 5/10
• 7.05 = 7 + 5/100

6. Conversions

Length:

• 1 cm = 10 mm → 1 mm = 0.1 cm
• 1 m = 100 cm → 1 cm = 0.01 m

Weight:

• 1 kg = 1000 g → 1 g = 0.001 kg

Money:

• 1 rupee = 100 paise → 1 paise = 0.01 rupee

7. Comparing Decimals

Compare from left to right by place value.

Example:

• 6.456 < 6.465

Zeros on the right side (after the decimal) do not change the value:

• 0.2 = 0.20 = 0.200

8. Decimals on Number Line

• 1.4 lies between 1 and 2.
• Divide the unit into 10 parts for tenths, 100 parts for hundredths.

9. Real Life Uses

Decimal mistakes can cause:

• Medical errors
• Flight issues
• Wrong product sizes

Example: 2.5 feet ≠ 2 ft 5 inche

10. Important Decimal Facts