Decimals — for Class 6

What Are Decimals — and Why Do They Exist?

Whole numbers like 5, 12, or 100 are comfortable. But the real world doesn’t always deal in whole numbers. Your height might be 142.5 cm. A bottle of juice might hold 1.5 litres. A cricket average might be 54.7. These are decimals — a way to write numbers that are between two whole numbers.

The word “decimal” comes from the Latin decem, meaning ten. Our entire number system is base-10 (the decimal number system), so decimals fit naturally into it.

Think of it this way: when we move one place to the right in our place value chart, the value becomes ten times smaller. After the units place, the next place is ten times smaller than 1 — that’s $\frac{1}{10}$ , written as the tenths place. And we use a dot (the decimal point) to mark where the whole number ends and the fractional part begins.

This is the single most important idea in this chapter: the decimal point is just a separator between the whole part and the fractional part. Once you see it that way, decimals stop being mysterious.

Key Terms and Definitions

Decimal point — the dot (.) that separates the whole number part from the fractional part. In 3.7, the point sits between 3 and 7.

Decimal number — any number that has a decimal point. Examples: 0.5, 12.34, 100.007.

Tenths place — the first digit after the decimal point. In 4.3, the digit 3 is in the tenths place, meaning $\frac{3}{10}$ .

Hundredths place — the second digit after the decimal point. In 4.37, the digit 7 is in the hundredths place, meaning $\frac{7}{100}$ .

Thousandths place — the third digit after the decimal point. Rarely tested at Class 6, but good to know.

Like decimals — decimals with the same number of decimal places. 2.30 and 5.47 are like decimals (both have two decimal places). We use this when adding or subtracting.

Unlike decimals — decimals with different numbers of decimal places. 3.5 and 2.47 are unlike decimals. Convert them to like decimals before operating.

The Place Value Table

Here’s how 47.83 fits into the extended place value chart:

Tens	Units	.	Tenths	Hundredths
4	7	.	8	3

So $47.83 = 40 + 7 + \frac{8}{10} + \frac{3}{100}$

Every whole number is already a decimal — just with .0 at the end. So 5 = 5.0 = 5.00. This becomes useful when you need to make unlike decimals into like decimals.

Core Concepts and Methods

Concept 1: Converting Fractions to Decimals

The fraction $\frac{7}{10}$ is read as “seven-tenths”. As a decimal: 0.7.

The pattern:

Denominator 10 → 1 decimal place: $\frac{3}{10} = 0.3$
Denominator 100 → 2 decimal places: $\frac{47}{100} = 0.47$
Denominator 1000 → 3 decimal places: $\frac{503}{1000} = 0.503$

What about $\frac{5}{100}$ ? The numerator is 5, but we need two decimal places. So we write 0.05 — the zero is a placeholder holding the tenths place.

Students often write $\frac{5}{100}$ as 0.5 instead of 0.05. Remember: the number of digits after the decimal point must equal the number of zeros in the denominator.

Concept 2: Converting Decimals to Fractions

Reverse the process:

0.7 = \frac{7}{10}

0.43 = \frac{43}{100}

2.5 = \frac{25}{10} = \frac{5}{2}

For mixed decimals like 2.5: the whole number (2) combines with the fractional part (0.5 = $\frac{5}{10}$ ), giving $2\frac{5}{10}$ or $\frac{25}{10}$ .

Concept 3: Comparing Decimals

Step 1: Compare the whole number parts. The larger whole number wins. Step 2: If whole numbers are equal, compare the tenths digit. Step 3: If tenths are equal, compare the hundredths digit. And so on.

To compare 3.72 and 3.68:

Whole parts: both are 3. Move on.
Tenths: 7 > 6. So 3.72 > 3.68.

When comparing, first make both decimals like decimals by adding trailing zeros. Compare 0.7 and 0.65 by writing them as 0.70 and 0.65. Now it’s clear: 70 hundredths > 65 hundredths, so 0.7 > 0.65.

Concept 4: Addition of Decimals

The rule is simple: line up the decimal points, then add column by column.

Why? Because we can only add tenths to tenths and hundredths to hundredths — just like we can only add tens to tens in regular addition.

To add 2.45 + 3.8:

Make them like decimals: 2.45 and 3.80
Line up decimal points and add:

  2.45
+ 3.80
------
  6.25

Concept 5: Subtraction of Decimals

Same rule: line up the decimal points, convert to like decimals, subtract.

To subtract 5.2 − 3.47:

Make like decimals: 5.20 − 3.47
Subtract with borrowing:

  5.20
- 3.47
------
  1.73

Comparing: Make like decimals → compare digit by digit from left to right

Adding/Subtracting: Make like decimals → align decimal points → operate column by column

Converting: $\frac{a}{10} = 0.a$ | $\frac{a}{100} = 0.0a$ if $a < 10$ , else $0.ab$

Solved Examples

Example 1 (CBSE — Easy)

Write 0.6 as a fraction in simplest form.

0.6 = \frac{6}{10} = \frac{3}{5}

Divide numerator and denominator by 2 to simplify.

Example 2 (CBSE — Easy)

Arrange in ascending order: 0.7, 0.07, 0.77, 0.007

Make all four decimals have three decimal places: 0.700, 0.070, 0.770, 0.007

Comparing: 7 < 70 < 700 < 770 (in thousandths)

Ascending order: 0.007, 0.07, 0.7, 0.77

Example 3 (CBSE — Easy)

Rahim walked 2.35 km in the morning and 1.7 km in the evening. Total distance?

2.35 + 1.70 = 4.05 \text{ km}

Example 4 (CBSE — Medium)

A ribbon is 8.5 m long. Priya cuts 3.75 m from it. How much ribbon remains?

8.50 - 3.75 = 4.75 \text{ m}

Make like decimals first (8.5 → 8.50), then subtract with borrowing in the hundredths column.

Example 5 (CBSE — Medium)

Express $\frac{235}{100}$ as a decimal and mark it on the number line.

\frac{235}{100} = 2.35

On the number line: 2.35 lies between 2 and 3. It’s 3 tenths and 5 hundredths past 2 — so past the 2.3 mark, 5 small divisions further (each small division = 0.01).

Example 6 (CBSE — Medium)

Which is greater: $\frac{3}{5}$ or 0.65?

Convert $\frac{3}{5}$ to a decimal. Multiply numerator and denominator by 20 to get denominator 100:

\frac{3}{5} = \frac{60}{100} = 0.60

Now compare: 0.60 vs 0.65 → 0.65 is greater.

Exam-Specific Tips

CBSE Class 6 Pattern: In your NCERT exam, decimals questions are worth 1–2 marks each. The most common question types are: (1) convert fraction ↔ decimal, (2) arrange in order, (3) word problems on money and measurement. Word problems on money (₹ and paise) and length (km, m, cm) are the most scoring — they appear in almost every paper.

Money connections: ₹1 = 100 paise. So ₹3.75 means 3 rupees and 75 paise. This is a decimal! CBSE loves combining decimals with real-life contexts like shopping or measurement.

Measurement connections: 1 km = 1000 m, so 1 m = 0.001 km. Similarly, 1 cm = 0.01 m. These conversions directly use decimal place values and show up in word problems every year.

Marking scheme: In Class 6 CBSE, most decimal questions are 1-mark or 2-mark. For 2-mark questions, write each step — show the like-decimal conversion, show the alignment. Don’t just write the answer.

Class 7 and Class 8 will build multiplication and division of decimals on top of what you learn now. Getting the place value logic solid at Class 6 means those chapters will feel easy. Students who rush through Class 6 decimals always struggle later.

Common Mistakes to Avoid

Mistake 1: Forgetting placeholder zeros

$\frac{3}{100}$ is NOT 0.3. It is 0.03. The zero in the tenths place is a placeholder — it tells us the 3 is in the hundredths place, not the tenths place. Always count: the number of decimal digits must equal the number of zeros in the denominator.

Mistake 2: Adding decimals without aligning

Adding 2.5 + 1.75 by writing 25 + 175 = 200 and then guessing where to put the decimal point is a recipe for errors. Always align the decimal points first — the decimal point in the answer is directly below the decimal points in the problem.

Mistake 3: Comparing by length instead of value

Thinking 0.75 > 0.8 because 75 > 8. This is wrong. Once you make like decimals — 0.75 vs 0.80 — it’s clear that 0.80 > 0.75. Never compare the digit count; compare the actual digit values position by position.

Mistake 4: Dropping trailing zeros when comparing

Some students “simplify” 0.80 to 0.8 mid-comparison and then get confused. Keep trailing zeros only for the purpose of making like decimals during comparison or operations. 0.80 and 0.8 represent the same number — but writing 0.80 helps when comparing with 0.83.

Mistake 5: Wrong placement after subtraction

In 5.20 − 3.47, students sometimes write 1.37 (off by a bit in borrowing). Always borrow carefully: 0 in hundredths can’t give 7, so borrow from tenths. But tenths has 2, which then becomes 1, and the hundredths becomes 10. Now 10 − 7 = 3. Then 1 − 4 requires borrowing from units. Practice this slowly once — it becomes automatic.

Practice Questions

Q1. Write 0.9 as a fraction.

$0.9 = \frac{9}{10}$

Q2. Convert $\frac{17}{100}$ to a decimal.

$\frac{17}{100} = 0.17$

The denominator is 100, so we need 2 decimal places. 17 already has two digits, so it goes directly: 0.17.

Q3. Which is smaller: 0.5 or 0.50?

They are equal. $0.5 = 0.50 = \frac{5}{10} = \frac{50}{100}$ . Adding a trailing zero after the last decimal digit never changes the value.

Q4. Arrange in descending order: 1.9, 1.09, 1.90, 1.009

Make all three decimal places: 1.900, 1.090, 1.900, 1.009

Note: 1.9 and 1.90 are the same number.

Descending order: 1.9, 1.90 (tied), 1.09, 1.009

If the question expects 4 distinct values, the list would be: 1.9, 1.09, 1.009 (with 1.9 = 1.90 noted).

Q5. Add: 4.73 + 2.8

Convert to like decimals: 4.73 + 2.80

  4.73
+ 2.80
------
  7.53

Answer: 7.53

Q6. Subtract: 10 − 4.38

Write 10 as 10.00:

  10.00
-  4.38
-------
   5.62

Answer: 5.62

(Borrow twice: from tenths to hundredths, then from units to tenths, then from tens to units.)

Q7. Riya has ₹54.50. She spends ₹32.75 on books. How much does she have left?

54.50 - 32.75

  54.50
- 32.75
-------
  21.75

Riya has ₹21.75 remaining.

Q8. A pipe is 6 m long. A plumber cuts two pieces of length 1.35 m and 2.6 m. What length of pipe remains?

Total cut = 1.35 + 2.60 = 3.95 m

Remaining = 6.00 − 3.95 = 2.05 m

Q9. Express 5 cm as metres using decimals. (1 m = 100 cm)

5 \text{ cm} = \frac{5}{100} \text{ m} = 0.05 \text{ m}

Q10. The temperature on Monday was 37.4°C. On Tuesday it was 0.85°C higher. What was Tuesday’s temperature?

37.40 + 0.85 = 38.25°\text{C}

Tuesday’s temperature was 38.25°C.

Frequently Asked Questions

What is the difference between 0.5 and 0.50?

They are identical. $0.5 = \frac{5}{10}$ and $0.50 = \frac{50}{100} = \frac{5}{10}$ . Trailing zeros after the last significant digit in a decimal don’t change its value. We add them only when we need like decimals for comparison or arithmetic.

How do I read a decimal number aloud?

Read the whole number part normally, say “point”, then read each digit after the decimal individually. So 3.47 is read as “three point four seven” — not “three point forty-seven”. (Though “three and forty-seven hundredths” is also correct and more formal.)

Is zero a decimal?

Zero is a whole number. But 0.0, 0.00 etc. are decimal representations of zero. In practice, when we say “decimal number” in Class 6, we mean a number like 2.5 or 0.7 — one that has a non-zero fractional part.

How do decimals connect to fractions?

Every decimal is a fraction whose denominator is a power of 10 (10, 100, 1000…). The decimal system is just a shorthand notation for these fractions. $0.7 = \frac{7}{10}$ , $0.47 = \frac{47}{100}$ . This is why the place value positions are called tenths, hundredths, thousandths.

Why do we line up decimal points when adding?

Because we must add like to like. Tenths can only be added to tenths, hundredths to hundredths — just as in whole number addition, tens are added to tens. The decimal point is the anchor that keeps all digits in their correct positions.

Can a decimal be negative?

Yes, though you won’t see negative decimals much in Class 6. −0.5 means half a unit below zero. Temperature problems in higher classes use these.

What comes after the thousandths place?

Ten-thousandths (0.0001), hundred-thousandths, and so on — each place is 10 times smaller than the previous. At Class 6, you only need to know tenths and hundredths confidently. Thousandths appear occasionally in measurement conversions.

How is 1.0 different from 1?

Mathematically, they are the same number. But writing 1.0 explicitly tells the reader that the measurement is precise to one decimal place — this matters in science. In pure maths, 1 = 1.0 = 1.00.