Decimals (Grade 5)
Decimals are numbers that have a whole-number part and a fractional part separated by a decimal point (.). For example, 3.75 means 3 whole and 75 hundredths.
You already use decimals every day without realising it. When you see a price tag of Rs.49.50, a height measurement of 1.35 m, or a temperature of 36.6°C, you are reading decimal numbers. The decimal point tells you where the whole numbers end and the fractional parts begin.
In Class 5, you will study decimal place values up to thousandths, learn to read and write decimals in words, convert between fractions and decimals, write decimals in expanded form, and understand equivalent decimals. This chapter forms the foundation for decimal operations (addition, subtraction, multiplication, and division) that follow.
What is Decimals - Class 5 Maths (Decimals)?
A decimal number uses a dot (called the decimal point) to separate the whole-number part from the fractional part.
Decimal number = Whole part . Fractional part
Example: 24.375 = 24 + 3/10 + 7/100 + 5/1000
Place value chart for decimals:
| Tens | Ones | . | Tenths (1/10) | Hundredths (1/100) | Thousandths (1/1000) |
|---|---|---|---|---|---|
| 2 | 4 | . | 3 | 7 | 5 |
Each place to the right of the decimal is 1/10 of the place to its left, just as each place to the left is 10 times the one to its right. This pattern extends the base-10 system into the fractional world.
Decimals (Grade 5) Formula
Key decimal-fraction relationships:
1 tenth = 1/10 = 0.1
1 hundredth = 1/100 = 0.01
1 thousandth = 1/1000 = 0.001
Reading decimals:
- 0.3 is read as "zero point three" or "three tenths".
- 4.56 is read as "four point five six" or "four and fifty-six hundredths".
- 1.025 is read as "one point zero two five" or "one and twenty-five thousandths".
Converting a fraction to a decimal: Divide the numerator by the denominator using long division. Or make the denominator 10, 100, or 1000 if possible.
Converting a decimal to a fraction:
- Count the number of digits after the decimal point.
- Write those digits over the matching power of 10 (1 digit → /10, 2 digits → /100, 3 digits → /1000).
- Simplify the fraction by dividing numerator and denominator by their GCD.
Expanded form: Write each digit multiplied by its place value. Example: 3.46 = 3 + 4/10 + 6/100 = 3 + 0.4 + 0.06.
Types and Properties
Types of decimals studied in Class 5:
- Tenths (1 decimal place): 0.5, 3.2, 7.9 — each digit after the decimal represents 1/10. Common in everyday measurement.
- Hundredths (2 decimal places): 0.25, 6.08, 12.50 — used in money (Rs.45.75 means 45 rupees and 75 paise).
- Thousandths (3 decimal places): 0.125, 4.003, 9.750 — used in science and precise measurement.
Equivalent decimals: Adding zeros to the right of the last decimal digit does not change the value.
0.5 = 0.50 = 0.500
This is because 5/10 = 50/100 = 500/1000 — they are all equivalent fractions.
Like and unlike decimals:
- Like decimals have the same number of decimal places: 3.45, 7.82, 0.16 (all have 2 decimal places).
- Unlike decimals have different numbers of decimal places: 2.5, 3.08, 1.125. Convert to like decimals by adding trailing zeros: 2.500, 3.080, 1.125.
Solved Examples
Example 1: Example 1: Writing a Decimal from Place Values
Problem: Write the decimal for: 3 ones, 4 tenths, 0 hundredths, 7 thousandths.
Solution:
Step 1: Ones place = 3, Tenths = 4, Hundredths = 0, Thousandths = 7
Step 2: Combine: 3.407
Reading: "Three and four hundred seven thousandths" or "three point four zero seven."
Answer: 3.407
Example 2: Example 2: Identifying Place Value of a Digit
Problem: In 56.839, what is the place value of 3?
Solution:
Step 1: Identify the position of 3. After the decimal: 8 is in the tenths place, 3 is in the hundredths place, 9 is in the thousandths place.
Step 2: Place value of 3 = 3 hundredths = 3/100 = 0.03
Note: The face value of the digit is 3, but its place value is 0.03 because it occupies the hundredths position.
Answer: The place value of 3 in 56.839 is 3 hundredths (0.03).
Example 3: Example 3: Converting a Fraction to a Decimal
Problem: Express 3/4 as a decimal.
Solution:
Method 1 (Division): Divide 3 by 4. 3 ÷ 4 = 0.75
Method 2 (Equivalent fraction): 3/4 = (3 × 25)/(4 × 25) = 75/100 = 0.75
Both methods give: 0.75
Answer: 3/4 = 0.75
Example 4: Example 4: Converting a Decimal to a Fraction
Problem: Express 0.125 as a fraction in simplest form.
Solution:
Step 1: 0.125 has 3 decimal places, so write 125 over 1000: 0.125 = 125/1000
Step 2: Find GCD of 125 and 1000. 125 = 5 × 5 × 5 and 1000 = 8 × 125. GCD = 125.
Step 3: Simplify: 125 ÷ 125 = 1, 1000 ÷ 125 = 8. So 125/1000 = 1/8.
Answer: 0.125 = 1/8
Example 5: Example 5: Expanded Form of a Decimal
Problem: Write 42.635 in expanded form.
Solution:
Step 1: Break down each digit by its place value:
- 4 in tens = 40
- 2 in ones = 2
- 6 in tenths = 6/10 = 0.6
- 3 in hundredths = 3/100 = 0.03
- 5 in thousandths = 5/1000 = 0.005
Step 2: 42.635 = 40 + 2 + 0.6 + 0.03 + 0.005
Answer: 40 + 2 + 0.6 + 0.03 + 0.005
Example 6: Example 6: Placing a Decimal on a Number Line
Problem: Mark 2.7 on a number line between 2 and 3.
Solution:
Step 1: Divide the segment from 2 to 3 into 10 equal parts. Each part represents 0.1.
Step 2: Starting from 2, count 7 parts to the right: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7.
2.0 — 2.1 — 2.2 — 2.3 — 2.4 — 2.5 — 2.6 — 2.7 — 2.8 — 2.9 — 3.0
Answer: 2.7 is located 7 tenths after 2 on the number line. It is closer to 3 than to 2.
Example 7: Example 7: Equivalent Decimals
Problem: Are 3.50 and 3.5 the same? Explain.
Solution:
Step 1: 3.50 = 3 + 50/100 = 3 + 1/2
Step 2: 3.5 = 3 + 5/10 = 3 + 1/2
Both equal 3 1/2. Adding a zero at the end of a decimal does not change its value. These are called equivalent decimals.
More examples: 7.0 = 7, 0.90 = 0.9, 1.200 = 1.2
Answer: Yes, 3.50 = 3.5. They are equivalent decimals.
Example 8: Example 8: Decimal in Money Context
Problem: Dev has Rs.45.60. Express the paise part as a fraction of a rupee in simplest form.
Solution:
Step 1: Rs.45.60 means 45 rupees and 60 paise.
Step 2: 1 rupee = 100 paise. So 60 paise = 60/100 of a rupee.
Step 3: Simplify: 60/100 = 3/5 (divide both by 20).
Answer: The paise part is 3/5 of a rupee (which is 0.60 in decimal form).
Example 9: Example 9: Decimal in Measurement
Problem: Neha measures a pencil as 17.5 cm. Express this length in metres as a decimal.
Solution:
Step 1: 1 metre = 100 cm. So to convert cm to m, divide by 100.
Step 2: 17.5 cm = 17.5 ÷ 100 = 0.175 m
Explanation: Dividing by 100 moves the decimal point 2 places to the left: 17.5 → 1.75 → 0.175.
Answer: 17.5 cm = 0.175 m
Example 10: Example 10: Writing a Decimal in Words
Problem: Write 108.046 in words.
Solution:
Step 1: Whole part: 108 = "one hundred eight"
Step 2: Decimal part: 046 thousandths. The 0 is a placeholder. 046 = 46.
Step 3: So 108.046 = "one hundred eight and forty-six thousandths."
Alternative reading: "One hundred eight point zero four six."
Answer: One hundred eight and forty-six thousandths.
Real-World Applications
Where do we use decimals in daily life?
- Money: Rs.99.50 means 99 rupees and 50 paise. All prices, bills, and bank statements use decimals.
- Measurement: Height (1.35 m), weight (42.5 kg), distance (3.7 km), volume (1.5 litres). Science and medicine rely heavily on decimal precision.
- Temperature: Normal body temperature is 36.6°C. Weather reports use decimals for daily temperatures.
- Sports: A cricket run rate of 8.25 runs per over. A 100 m race won in 10.49 seconds.
- Fuel and petrol: Petrol costs Rs.105.72 per litre. The odometer reading might show 12345.6 km.
- Cooking: Recipes may require 0.5 kg of sugar or 0.25 litres of milk.
Key Points to Remember
- A decimal point separates the whole-number part from the fractional part.
- Place values after the decimal: tenths (1/10), hundredths (1/100), thousandths (1/1000), moving left to right.
- Each decimal place is 1/10 of the place to its left.
- Adding trailing zeros to the right of a decimal does not change its value (0.5 = 0.50 = 0.500).
- To convert a fraction to a decimal: divide the numerator by the denominator.
- To convert a decimal to a fraction: write over the appropriate power of 10 and simplify.
- Decimals are used extensively in money, measurement, sports, science, and cooking.
- In the Indian money system: 1 rupee = 100 paise, so paise are always expressed as hundredths of a rupee.
Practice Problems
- Write the decimal for: 5 tens, 2 ones, 8 tenths, 0 hundredths, 3 thousandths.
- What is the place value of 6 in 73.264?
- Express 7/8 as a decimal using long division.
- Express 0.45 as a fraction in simplest form.
- Write 305.019 in expanded form using place values.
- Mark 1.4 on a number line between 1 and 2. How many tenths is it from 1?
- Ria bought a notebook for Rs.32.75 and a pen for Rs.15.50. Express the paise part of each price as a fraction of one rupee.
- Arrange in ascending order: 3.05, 3.5, 3.005, 3.50.
Frequently Asked Questions
Q1. What is a decimal number?
A decimal number has a whole-number part and a fractional part separated by a decimal point. For example, 6.35 has whole part 6 and fractional part 35 hundredths (0.35).
Q2. What are tenths, hundredths, and thousandths?
These are place values after the decimal point. The first position is tenths (1/10 = 0.1), the second is hundredths (1/100 = 0.01), and the third is thousandths (1/1000 = 0.001). Each position is 10 times smaller than the one before it.
Q3. Is 0.5 the same as 0.50?
Yes. Adding zeros to the right of the last decimal digit does not change the value. 0.5 = 0.50 = 0.500 = 5/10 = 1/2. These are called equivalent decimals.
Q4. How do I convert a fraction to a decimal?
Divide the numerator by the denominator using long division. For example, 3/8: divide 3.000 by 8 to get 0.375. Alternatively, make the denominator 10 or 100 (e.g., 3/4 = 75/100 = 0.75).
Q5. How do I convert a decimal to a fraction?
Count the decimal places. Write the digits after the decimal over the matching power of 10. Simplify. For example, 0.75 = 75/100. GCD of 75 and 100 is 25. So 75/100 = 3/4.
Q6. Why is the decimal system based on 10?
Our number system is base-10 (each place value is 10 times the one to its right). Decimals simply extend this same pattern to the right of the ones place, giving tenths, hundredths, and thousandths.
Q7. How do decimals relate to Indian money?
In Indian currency, 1 rupee = 100 paise. So Rs.5.75 means 5 rupees and 75 paise. The decimal part (0.75) represents 75 hundredths of a rupee = 75 paise.
Q8. What is the difference between 3.4 and 3.04?
3.4 means 3 and 4 tenths (3 + 0.4 = 3.40), while 3.04 means 3 and 4 hundredths (3 + 0.04). Since 0.4 = 0.40 > 0.04, we have 3.4 > 3.04. The zero in 3.04 is a placeholder in the tenths position.
Q9. Is this topic in the NCERT Class 5 syllabus?
Yes. Decimals is a major chapter in the NCERT/CBSE Class 5 Maths curriculum. Students learn place values, fraction-decimal conversions, and basic operations with decimals.
Related Topics
- Introduction to Decimals
- Comparing and Ordering Decimals
- Addition of Decimals
- Subtraction of Decimals
- Multiplication of Decimals
- Division of Decimals
- Converting Fractions to Decimals (Grade 5)
- Converting Decimals to Fractions
- Decimal Word Problems (Grade 5)
- Decimal Place Value (Grade 5)
- Rounding Decimals
- Multiplying Decimals by 10, 100 and 1000
