What Are Decimals?
Decimals are numbers that have a dot (.) called a decimal point.
They are used to show parts of a whole, just like fractions.
For example:
• 1.
5 means 1 whole and half, like 1½.
• 0.
75 means 75 out of 100 parts, like 75 paise is ₹0. 75!
Why Are Decimals Important?
Decimals are used in many real-life situations:
• When measuring your height: 4.
5 feet
• When buying vegetables: 1.
25 kg
• When you see prices: ₹5.
99
• When checking time: 1.
5 hours
Learning about comparing decimals and how to shift decimals is really useful.
Place Value in Decimals
Remember:
Each digit has a place.
The decimal point separates the number into two parts:
• Left of the point = Whole numbers
• Right of the point = Decimal values
Place Value Table:
Place Thousands Hundreds Tens Ones .
Tenths Hundredths Thousandths
Number 3 5 2 7 .
8 1 6
Value 3000 500 20 7 .
0. 8 0. 01 0. 006
So, the number 3527.
816 means:
• 3,000 + 500 + 20 + 7 + 0.
8 + 0. 01 + 0. 006
Comparing Decimals
When we compare two decimal numbers, we find out which one is bigger or smaller.
Steps to Compare Decimals:
1.Compare the whole numbers.
• Bigger whole number = bigger decimal number.
Example:
• 3.
25 > 2. 99 (Because 3 > 2)
2.If whole numbers are the same, compare tenths.
Example:
• 5.
7 vs 5. 4 → Compare 7 and 4 → 5. 7 > 5. 4
3. If tenths are the same, compare hundredths.
Example:
• 3.
25 vs 3. 29 → 25 vs 29 → 3. 29 > 3. 25
4. Add zeroes if needed.
Example:
• 3.
2 vs 3. 20 → They are equal
Helpful Tip:
Line up the numbers by the decimal point before comparing.
Examples:
1.
2. 3 vs 2. 45 → 2. 30 vs 2. 45 → 2. 30 < 2. 45
2.
0. 75 vs 0. 705 → 0. 750 vs 0. 705 → 750 > 705 → 0. 75 > 0. 705
3.
1. 05 vs 1. 5 → 1. 05 < 1. 50 → So, 1. 05 < 1. 5
Decimal Shift
Decimal Shift means moving the decimal point to make the number bigger or smaller by 10, 100, or 1000.
When Do We Shift the Decimal?
When we multiply or divide decimals by 10, 100, 1000…
Move the decimal point right when multiplying.
Move the decimal point left when dividing.
Decimal Shift While Multiplying
Rule:
When we multiply a decimal by 10, 100, or 1000 → Move decimal to the RIGHT.
Examples:
1.
2. 5 × 10 = 25. 0 (Decimal shifts 1 place right)
2.
3. 47 × 100 = 347 (Shift 2 places right)
3.
0. 789 × 1000 = 789 (Shift 3 places right)
Decimal Shift While Dividing
Rule:
When we divide a decimal by 10, 100, or 1000 → Move decimal to the LEFT.
Examples:
1.
25. 0 ÷ 10 = 2. 5 (Decimal shifts 1 place left)
2.
347 ÷ 100 = 3. 47 (Shift 2 places left)
