Class 7 | Ganita Prakash | Chapter 3
🔢 A Peek Beyond the Point
Decimals · Tenths · Hundredths · Measurement
📏 3.1 — Why Do We Need Smaller Units?
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📖 The Story!
A child wants to measure a small jewel or screw — but whole numbers aren't enough!
We need numbers between 0 and 1 → Decimals!
A child wants to measure a small jewel or screw — but whole numbers aren't enough!
We need numbers between 0 and 1 → Decimals!
Whole units are too big for small things!
- Width of a pencil ≈ 0.7 cm
- Thickness of a coin ≈ 0.2 cm
- Weight of a tablet ≈ 0.5 grams
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1️⃣0️⃣ 3.2 — A Tenth Part (0.1)
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What is a Tenth?
Divide 1 into 10 equal parts
1 part = 1/10 = 0.1 (one tenth)
Divide 1 into 10 equal parts
1 part = 1/10 = 0.1 (one tenth)
1 ÷ 10 = 0.1
- 0.1 = one tenth
- 0.2 = two tenths = 2/10
- 0.5 = five tenths = half! 🎉
- 0.9 = nine tenths
- 1.0 = one whole
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💯 3.3 — A Hundredth Part (0.01)
What is a Hundredth?
Divide 1 into 100 equal parts
1 part = 1/100 = 0.01 (one hundredth)
Divide 1 into 100 equal parts
1 part = 1/100 = 0.01 (one hundredth)
1 ÷ 100 = 0.01
0.1 = 10/100 → so 0.1 is 10 times bigger than 0.01!
Place Values in Decimals:
7 3 . 4 5
→ 7 = Tens 3 = Ones 4 = Tenths 5 = Hundredths
Each place is 10 times the next one to the right!
7 3 . 4 5
→ 7 = Tens 3 = Ones 4 = Tenths 5 = Hundredths
Each place is 10 times the next one to the right!
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📍 3.4 — Decimal Place Value
| Number | Tens | Ones | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|
| 70.5 | 7 | 0 | 5 | — | — |
| 7.05 | — | 7 | 0 | 5 | — |
| 0.274 | — | 0 | 2 | 7 | 4 |
How to read decimals:
70.5 = "Seventy point five" (= seventy and five-tenths)
7.05 = "Seven point zero five" (seven and five-hundredths)
0.274 = "Zero point two seven four" (NOT "zero point 274"!)
70.5 = "Seventy point five" (= seventy and five-tenths)
7.05 = "Seven point zero five" (seven and five-hundredths)
0.274 = "Zero point two seven four" (NOT "zero point 274"!)
🧠 Think of it like money!
₹7.05 = 7 rupees and 5 paise
₹0.75 = 75 paise = three-quarters of a rupee
Decimals in real life = MONEY! 💰
₹7.05 = 7 rupees and 5 paise
₹0.75 = 75 paise = three-quarters of a rupee
Decimals in real life = MONEY! 💰
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📐 3.5 — Units of Measurement
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| Unit | Relation | In Decimals |
|---|---|---|
| 1 mm | = 1/10 cm | 0.1 cm |
| 5 mm | = 5/10 cm | 0.5 cm |
| 1 cm | = 1/100 m | 0.01 m |
| 56 mm | = 5 cm + 6 mm | 5.6 cm |
| 1 g | = 1/1000 kg | 0.001 kg |
| 500 g | = half kg | 0.5 kg |
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🔍 3.6 — Locating & Comparing Decimals
On a Number Line:
Between 0 and 1, mark tenths: 0.1, 0.2, 0.3... 0.9, 1.0
Between 0.1 and 0.2, mark hundredths: 0.11, 0.12... 0.19, 0.20
Between 0 and 1, mark tenths: 0.1, 0.2, 0.3... 0.9, 1.0
Between 0.1 and 0.2, mark hundredths: 0.11, 0.12... 0.19, 0.20
How to Compare Decimals:
Example: 0.2 vs 0.02 vs 0.002
→ 0.2 = 0.200 0.02 = 0.020 0.002 = 0.002
→ 0.2 > 0.02 > 0.002
Compare the whole number part first
If equal, compare tenths digit
If equal, compare hundredths digit
Continue until different!
Example: 0.2 vs 0.02 vs 0.002
→ 0.2 = 0.200 0.02 = 0.020 0.002 = 0.002
→ 0.2 > 0.02 > 0.002
🎯 Adding zeros after the last decimal digit doesn't change value!
0.2 = 0.20 = 0.200 ✅
But: 0.2 ≠ 0.02 ❌ (These are different! Zero BEFORE digit matters!)
0.2 = 0.20 = 0.200 ✅
But: 0.2 ≠ 0.02 ❌ (These are different! Zero BEFORE digit matters!)
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📝 Quick Cheatsheet
0.1 = 1/10
One Tenth
→ 1 of 10 parts
One Tenth
→ 1 of 10 parts
0.01 = 1/100
One Hundredth
→ 1 of 100 parts
One Hundredth
→ 1 of 100 parts
1 mm = 0.1 cm
1 cm = 0.01 m
1 g = 0.001 kg
1 cm = 0.01 m
1 g = 0.001 kg
Compare left→right
digit by digit
after decimal!
digit by digit
after decimal!
| Place | Value | Example in 3.456 |
|---|---|---|
| Ones | 1 | 3 |
| Tenths | 1/10 = 0.1 | 4 → 0.4 |
| Hundredths | 1/100 = 0.01 | 5 → 0.05 |
| Thousandths | 1/1000 = 0.001 | 6 → 0.006 |
🌟 Chapter 3 Complete! 🌟
Made with ❤️ by @edugrown
Made with ❤️ by @edugrown