Class 5 | CBSE, NCERT & ICSE
Have you ever looked at the price of petrol? It says something like ₹104.50 per litre. What about your height — maybe 1.35 metres? Or the temperature on a hot day — 37.5°C? A cricket player's batting average might be 52.34. All of these numbers have a dot (called a decimal point) in the middle. These are called decimal numbers!
In Class 4, you were introduced to the idea of decimals. Now in Class 5, we will explore decimals deeply — learning their place values, how to convert between fractions and decimals, how to compare them, and how to add, subtract, multiply and divide them. Decimals are one of the most useful topics in mathematics because we use them every single day!
A decimal number is a number that has a whole part and a fractional part separated by a decimal point (.).
A decimal is simply another way of writing a fraction whose denominator is 10, 100, 1000, etc.
| Fraction | Decimal | How to Read |
|---|---|---|
| 3/10 | 0.3 | Zero point three (or three tenths) |
| 7/10 | 0.7 | Zero point seven (or seven tenths) |
| 45/100 | 0.45 | Zero point four five (or forty-five hundredths) |
| 8/100 | 0.08 | Zero point zero eight (or eight hundredths) |
| 125/1000 | 0.125 | Zero point one two five (or one hundred twenty-five thousandths) |
| 2 3/10 | 2.3 | Two point three (two and three tenths) |
Just as whole numbers have place values (ones, tens, hundreds), decimal numbers have place values to the right of the decimal point. Each place is 10 times smaller than the one before it.
| Hundreds | Tens | Ones | . (Decimal Point) | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|
| 100 | 10 | 1 | . | 1/10 = 0.1 | 1/100 = 0.01 | 1/1000 = 0.001 |
| H | T | O | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|
| 1 | 5 | 6 | . | 3 | 7 | 4 |
Place value of 1 = 1 × 100 = 100
Place value of 5 = 5 × 10 = 50
Place value of 6 = 6 × 1 = 6
Place value of 3 = 3 × 1/10 = 3/10 = 0.3
Place value of 7 = 7 × 1/100 = 7/100 = 0.07
Place value of 4 = 4 × 1/1000 = 4/1000 = 0.004
To read a decimal number, we read the whole number part first, say "point", and then read each digit of the decimal part one by one.
| Number | How to Read | In Words |
|---|---|---|
| 23.45 | Twenty-three point four five | Twenty-three and forty-five hundredths |
| 0.7 | Zero point seven | Seven tenths |
| 5.08 | Five point zero eight | Five and eight hundredths |
| 100.125 | One hundred point one two five | One hundred and one hundred twenty-five thousandths |
| 0.006 | Zero point zero zero six | Six thousandths |
| 72.9 | Seventy-two point nine | Seventy-two and nine tenths |
Decimals can be classified based on the number of digits after the decimal point (called decimal places).
We can make unlike decimals "like" by adding zeros at the end of the decimal part. Adding zeros after the last decimal digit does NOT change the value of the number!
Since decimals are just another way to write fractions with denominators 10, 100, or 1000, we can easily convert between them.
Simply write the numerator and place the decimal point so the correct number of digits are after it.
Make an equivalent fraction with 10, 100, or 1000 as the denominator, then convert.
Divide the numerator by the denominator. Add a decimal point and zeros as needed.
To convert a decimal to a fraction, count the number of decimal places and use the appropriate denominator. Then simplify (reduce) the fraction if possible.
To compare decimals, we compare digit by digit from left to right — just like comparing whole numbers, but we must line up the decimal points first.
Adding decimals is just like adding whole numbers — the key rule is to line up the decimal points one below the other. Then add column by column from right to left.
2 3 . 4 5
+ 7 . 3 0
---------
3 0 . 7 5
Answer: 30.75
1 5 6 . 8 0 0
+ 2 3 . 4 5 6
-------------
1 8 0 . 2 5 6
Answer: 180.256
4 5 . 0 0
+ 3 . 7 5
---------
4 8 . 7 5
Answer: 48.75
3 5 . 5 0
+ 1 2 . 7 5
---------
4 8 . 2 5
Meena spent ₹48.25 in total.
Subtracting decimals follows the same principle — line up the decimal points, make like decimals, then subtract column by column. Borrow when needed, just like with whole numbers.
4 5 . 7 8
- 2 3 . 4 5
---------
2 2 . 3 3
Answer: 22.33
5 0 . 0 0
- 2 3 . 6 5
---------
2 6 . 3 5
Answer: 26.35
8 . 3 0 0
- 4 . 5 6 7
---------
3 . 7 3 3
Answer: 3.733
1 0 0 . 0 0
- 6 7 . 5 0
-----------
3 2 . 5 0
Arjun got ₹32.50 as change.
When we multiply a decimal by 10, 100, or 1000, the decimal point moves to the right. This makes the number bigger.
If there aren't enough digits, add zeros.
When we divide a decimal by 10, 100, or 1000, the decimal point moves to the left. This makes the number smaller.
If there aren't enough digits, add zeros before the number.
Decimals appear in everyday life — especially when dealing with money, measurement, and weight. Let's solve some real-life problems:
8 5 . 5 0
6 2 . 7 5
+ 1 4 5 . 2 5
-----------
2 9 3 . 5 0
Sita spent ₹293.50 in total.
5 0 0 . 0 0
- 3 4 7 . 7 5
-----------
1 5 2 . 2 5
Arjun received ₹152.25 as change.
| Term | Meaning |
|---|---|
| Decimal | A number with a whole part and a fractional part separated by a decimal point |
| Decimal Point | The dot (.) that separates the whole number from the fractional part |
| Tenths | The first place after the decimal point (1/10 = 0.1) |
| Hundredths | The second place after the decimal point (1/100 = 0.01) |
| Thousandths | The third place after the decimal point (1/1000 = 0.001) |
| Like Decimals | Decimals with the same number of decimal places |
| Unlike Decimals | Decimals with different number of decimal places |
| Equivalent Decimals | Decimals that have the same value (e.g., 0.5 = 0.50 = 0.500) |
| Place Value | The value of a digit based on its position in the number |
| Expanded Form | A decimal written as the sum of the values of each digit |
Finished learning? Now test what you know!