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Decimals Operations and Applications

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Decimals Operations and Applications

Decimals Operations and Applications

Decimal place value chart illustration

📊 Part 1: Decimal Place Value and Identification

1. Write the following numbers in decimal form:

a) Three and four tenths: ___________

b) Seven and twenty-five hundredths: ___________

c) Nine and one hundred forty-three thousandths: ___________

2. Circle the largest decimal in each group:

Group A:

0.45
0.405
0.54

Group B:

2.8
2.08
2.80

Group C:

0.123
0.132
0.213

3. Order these decimals from smallest to largest:

3.45, 3.054, 3.5, 3.405

🧮 Part 2: Decimal Operations

4. Calculate the following additions. Show your working:

a) 12.45 + 8.7 = _______

b) 0.356 + 2.89 = _______

5. Calculate the following subtractions. Show your working:

a) 15.8 - 7.45 = _______

b) 9.02 - 3.456 = _______

6. Multiply these decimals by powers of 10:

a) 4.56 × 10 = _______

b) 0.789 × 100 = _______

c) 2.34 × 1000 = _______

d) 67.8 ÷ 10 = _______

e) 345.6 ÷ 100 = _______

🔄 Part 3: Converting Between Decimals, Fractions, and Percentages

7. Match each decimal with its equivalent fraction and percentage:
0.25
0.5
0.75
0.1
1/2 = 50%
3/4 = 75%
1/4 = 25%
1/10 = 10%
8. Convert the following:

a) 0.6 as a fraction: _______

b) 0.35 as a percentage: _______

c) 3/5 as a decimal: _______

d) 85% as a decimal: _______

💰 Part 4: Real-World Applications

9. Shopping Problem:

Sarah buys the following items at the supermarket:

• Apples: $4.65

• Bread: $2.80

• Milk: $3.45

• Cheese: $7.25

a) What is the total cost? Show your working:

b) If Sarah pays with a $20 note, how much change will she receive?

10. Sports Timing Problem:

In a 100-metre race, the finishing times were:

• Runner A: 12.45 seconds

• Runner B: 12.8 seconds

• Runner C: 12.05 seconds

• Runner D: 12.385 seconds

List the runners in order from fastest to slowest:

11. Cooking Problem:

A recipe calls for 2.5 kg of flour. If you want to make half the recipe, how much flour do you need?

12. Temperature Problem:

The temperature readings for a week were: 18.5°C, 19.2°C, 17.8°C, 20.1°C, 18.9°C, 19.6°C, 18.3°C

What was the average temperature for the week? (Round to 1 decimal place)

🎯 Part 5: Problem Solving and Estimation

13. Estimation Challenge:

Before calculating, estimate the answers to the nearest whole number:

a) 8.7 + 12.3 ≈ _____ (Estimate) Actual: _____

b) 15.8 - 6.2 ≈ _____ (Estimate) Actual: _____

c) 4.9 × 3 ≈ _____ (Estimate) Actual: _____

14. Which of the following statements are true? Check all that apply:

0.5 is greater than 0.05

2.30 equals 2.3

0.75 is the same as 3/4

1.5 × 10 = 15

0.1 + 0.1 + 0.1 = 0.3

15. Word Problem:

A school is organising a fun run. The track is 1.25 km long. If a student completes 3.5 laps, how many kilometres have they run in total?

16. Reflection:

Explain in your own words why it's important to line up decimal points when adding or subtracting decimals:

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