Word Problems on Decimals
Decimals are used everywhere — in money (Rs. 45.50), measurements (2.5 kg), distances (3.75 km), and temperature (37.2°C). Now that you know how to add, subtract, and compare decimals, it is time to solve word problems.
Word problems test whether you can use decimals in real situations. The approach is the same as with whole numbers — read the problem, decide the operation, calculate, and answer with the correct unit.
You will practise problems involving money, weight, length, and capacity.
What is Word Problems on Decimals?
Steps to solve decimal word problems:
- Read the problem carefully. Note all decimal numbers.
- Decide the operation: addition (total), subtraction (remaining/difference), comparison.
- Line up the decimal points when writing numbers vertically.
- Solve step by step.
- Write the answer with the correct unit.
Tips:
- Always align decimal points before adding or subtracting.
- Add trailing zeros to make decimal places equal (5.3 → 5.30).
- In money, use 2 decimal places (Rs. 45.50).
Types and Properties
1. Money Problems
Prices, bills, change, and savings involve decimals.
- Notebook Rs. 35.75 + Pen Rs. 12.50 = Rs. 48.25.
2. Weight Problems
- Rice 5.250 kg + Sugar 3.750 kg = 9.000 kg.
3. Distance Problems
- Home to school 2.30 km + School to park 1.85 km = 4.15 km.
- Jug 2.50 litres − poured out 0.75 litres = 1.75 litres.
Solved Examples
Example 1: Example 1: Total cost
Problem: Ravi bought a book for Rs. 125.50 and a bag for Rs. 340.75. Total spent?
Solution:
- 125.50 + 340.75 = 466.25
Answer: Rs. 466.25
Example 2: Example 2: Finding change
Problem: Meena gave Rs. 500 for groceries worth Rs. 387.60. Change?
Solution:
- 500.00 − 387.60 = 112.40
Answer: Rs. 112.40
Example 3: Example 3: Total weight
Problem: Wheat 10.500 kg + Sugar 5.250 kg. Total?
Solution:
- 10.500 + 5.250 = 15.750 kg
Answer: 15.750 kg
Example 4: Example 4: Weight difference
Problem: Suresh weighs 45.8 kg, his brother 38.5 kg. How much heavier?
Solution:
- 45.8 − 38.5 = 7.3 kg
Answer: 7.3 kg heavier.
Example 5: Example 5: Total distance
Problem: Anita cycled 3.75 km morning, 2.50 km evening. Total?
Solution:
- 3.75 + 2.50 = 6.25 km
Answer: 6.25 km
Example 6: Example 6: Remaining distance
Problem: Two cities are 150.5 km apart. Bus covered 98.75 km. How much left?
Solution:
- 150.50 − 98.75 = 51.75 km
Answer: 51.75 km
Example 7: Example 7: Capacity problem
Problem: Bucket has 8.5 litres. 3.75 litres used. How much left?
Solution:
- 8.50 − 3.75 = 4.75 litres
Answer: 4.75 litres
Example 8: Example 8: Comparison
Problem: Rope A = 12.45 m, Rope B = 9.80 m. Which is longer and by how much?
Solution:
- 12.45 > 9.80. Difference = 12.45 − 9.80 = 2.65 m.
Answer: Rope A is longer by 2.65 m.
Example 9: Example 9: Multi-step money
Problem: Rohit had Rs. 1000. Shirt Rs. 450.50, trousers Rs. 375.25. Money left?
Solution:
- Spent = 450.50 + 375.25 = 825.75.
- Left = 1000.00 − 825.75 = 174.25.
Answer: Rs. 174.25
Example 10: Example 10: Adding three decimals
Problem: Three parcels weigh 2.35 kg, 4.50 kg, and 1.15 kg. Total?
Solution:
- 2.35 + 4.50 + 1.15 = 8.00 kg
Answer: 8 kg
Real-World Applications
Shopping: Every bill uses decimals. Add prices for total, subtract from payment for change.
Cooking: Recipes use 0.5 litres milk, 1.25 kg flour. Adjusting quantities uses decimal operations.
Travel: Road signs show distances in decimals (45.5 km). Calculating remaining distance needs subtraction.
Health: Body weight (54.6 kg), temperature (98.6°F), medicine doses (2.5 ml) all use decimals.
Sports: Race times in decimals (11.58 seconds). Comparing times uses decimal subtraction.
Key Points to Remember
- Always align decimal points when adding or subtracting.
- Add trailing zeros to equalise decimal places.
- In money, use two decimal places.
- "Total" = add. "Remaining" = subtract. "More/less" = compare.
- Always include the unit in your answer.
- Check: does the answer make sense?
- Convert units if needed: 1 km = 1000 m, 1 kg = 1000 g.
Practice Problems
- Pencil Rs. 8.50 + eraser Rs. 3.75. Total cost? Change from Rs. 20?
- Watermelon 4.250 kg. Edible part 3.100 kg. Weight of rind?
- Sanya ran 2.75 km Monday, 3.50 km Tuesday. Total? How much more on Tuesday?
- Jug has 5 litres. Morning 1.75 litres used, evening 0.80 litres. How much left?
- Three books: Rs. 156.25, Rs. 89.50, Rs. 204.75. Total cost?
- Ram's height 1.52 m, Shyam's 1.68 m. Who is taller and by how much?
- Fuel tank holds 45.0 litres. After trip, 18.75 litres remain. Fuel used?
- Vegetables: potatoes 2.5 kg, onions 1.25 kg, tomatoes 0.750 kg. Total weight?
Frequently Asked Questions
Q1. Why align decimal points?
So you add ones to ones, tenths to tenths, hundredths to hundredths. Misalignment gives wrong answers.
Q2. What are trailing zeros?
Zeros at the end of a decimal (5.3 → 5.30). They do not change the value but make operations easier.
Q3. How to convert grams to kilograms?
Divide by 1000. 750 g = 0.750 kg. 250 g = 0.250 kg.
Q4. How to handle paise?
Write as decimal of rupees. 50 paise = Rs. 0.50. 75 paise = Rs. 0.75.
Q5. Can subtraction of whole numbers give a decimal?
Yes. 10 − 3.75 = 6.25. Write 10 as 10.00 first.
Q6. How to check decimal addition?
Add in a different order, or estimate by rounding. 3.75 + 2.50 ≈ 4 + 3 = 7, actual = 6.25.
Q7. What if a problem mixes decimals and fractions?
Convert to the same form. 1/2 = 0.5, 1/4 = 0.25. Then operate.
Q8. Are these problems in exams?
Yes. Word problems on decimals are common in Class 6 NCERT/CBSE exams.
