Class 7 | Ganita Prakash Part-II | Chapter 4
๐ข Another Peek Beyond the Point
Decimal Multiplication ยท Division ยท Powers of 10
๐ข 4.1 โ Quick Recap of Decimals
@edugrown
@edugrown
Decimals = Fractions with powers of 10!
3/10 = 0.3 4/100 = 0.04 67/1000 = 0.067
27.53 means:
2 Tens + 7 Ones + 5 Tenths + 3 Hundredths
= 20 + 7 + 0.5 + 0.03
3/10 = 0.3 4/100 = 0.04 67/1000 = 0.067
27.53 means:
2 Tens + 7 Ones + 5 Tenths + 3 Hundredths
= 20 + 7 + 0.5 + 0.03
๐ Jonali's Spice Game!
50g = 50/1000 kg = 0.050 kg
100g = 100/1000 kg = 0.100 kg
250g = 250/1000 kg = 0.250 kg
Decimals make small measurements easy!
50g = 50/1000 kg = 0.050 kg
100g = 100/1000 kg = 0.100 kg
250g = 250/1000 kg = 0.250 kg
Decimals make small measurements easy!
Dividing by 10, 100, 1000... (move decimal LEFT):
123 รท 10 = 12.3 (decimal moves 1 place left)
123 รท 100 = 1.23 (decimal moves 2 places left)
123 รท 1000 = 0.123 (decimal moves 3 places left)
123 รท 10 = 12.3 (decimal moves 1 place left)
123 รท 100 = 1.23 (decimal moves 2 places left)
123 รท 1000 = 0.123 (decimal moves 3 places left)
ใฐ๏ธใฐ๏ธใฐ๏ธ
โ๏ธ 4.2 โ Decimal Multiplication
@edugrown
How to Multiply Decimals:
Shortcut Rule:
Count total decimal places in both numbers โ that's how many in the answer!
0.3 (1 place) ร 0.4 (1 place) = 0.12 (2 places) โ
Convert decimals to fractions: 0.3 ร 0.4 = 3/10 ร 4/10
Multiply the fractions: = 12/100
Convert back to decimal: = 0.12
Shortcut Rule:
Count total decimal places in both numbers โ that's how many in the answer!
0.3 (1 place) ร 0.4 (1 place) = 0.12 (2 places) โ
More Examples:
9.5 ร 5: Ignore decimals โ 95 ร 5 = 475 โ 1 decimal place โ 47.5
1.64 ร 6: 164 ร 6 = 984 โ 2 decimal places โ 9.84
5.7 ร 13.3: 57 ร 133 = 7581 โ 2 decimal places โ 75.81
9.5 ร 5: Ignore decimals โ 95 ร 5 = 475 โ 1 decimal place โ 47.5
1.64 ร 6: 164 ร 6 = 984 โ 2 decimal places โ 9.84
5.7 ร 13.3: 57 ร 133 = 7581 โ 2 decimal places โ 75.81
@edugrown
@edugrown
ใฐ๏ธใฐ๏ธใฐ๏ธ
๐ Multiplying by 10, 100, 1000
Move decimal point RIGHT when multiplying:
| Multiply by | Move decimal | Example |
|---|---|---|
| 10 | 1 place RIGHT โ | 2.34 ร 10 = 23.4 |
| 100 | 2 places RIGHT โโ | 2.34 ร 100 = 234 |
| 1000 | 3 places RIGHT โโโ | 2.34 ร 1000 = 2340 |
Divide = move LEFT, Multiply = move RIGHT!
รท10 โ โ one place ร10 โ โ one place
รท100 โ โ two places ร100 โ โ two places
Count zeros = count places!
รท10 โ โ one place ร10 โ โ one place
รท100 โ โ two places ร100 โ โ two places
Count zeros = count places!
ใฐ๏ธใฐ๏ธใฐ๏ธ
โ 4.3 โ Decimal Division
@edugrown
Dividing a Decimal by Whole Number:
9.9 รท 3 = 3.3 (just divide, keep decimal in same position)
Dividing by a Decimal:
Convert divisor to whole number by multiplying both!
0.9 รท 0.3 = (0.9ร10) รท (0.3ร10) = 9 รท 3 = 3
7.5 รท 2.5 = 75 รท 25 = 3
9.9 รท 3 = 3.3 (just divide, keep decimal in same position)
Dividing by a Decimal:
Convert divisor to whole number by multiplying both!
0.9 รท 0.3 = (0.9ร10) รท (0.3ร10) = 9 รท 3 = 3
7.5 รท 2.5 = 75 รท 25 = 3
@edugrown
@edugrown
Long Division with Decimals:
If dividing decimal by whole: divide normally, place decimal in quotient directly above dividend decimal
If dividing by decimal: multiply both by 10/100/1000 to make divisor a whole number
Then do normal long division
ใฐ๏ธใฐ๏ธใฐ๏ธ
๐ Quick Cheatsheet
ร decimals:
Ignore decimal,
count places at end
Ignore decimal,
count places at end
ร10 โ move . right 1
ร100 โ right 2
ร1000 โ right 3
ร100 โ right 2
ร1000 โ right 3
รท10 โ move . left 1
รท100 โ left 2
รท1000 โ left 3
รท100 โ left 2
รท1000 โ left 3
รท decimal:
รboth to remove ..
then divide!
รboth to remove ..
then divide!
| Operation | Rule | Example |
|---|---|---|
| ร two decimals | Multiply without dots, count total decimal places | 1.2 ร 0.3 = 0.36 (2 places) |
| ร by 10โฟ | Shift decimal n places right | 4.56 ร 100 = 456 |
| รท by 10โฟ | Shift decimal n places left | 456 รท 100 = 4.56 |
| รท decimal | Multiply both by power of 10 first | 0.6 รท 0.2 = 6 รท 2 = 3 |
๐ Chapter 4 Complete! ๐
Made with โค๏ธ by @edugrown
Made with โค๏ธ by @edugrown