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Unit 3 Advanced Worksheet

Decimal Challenges

Challenge yourself with complex decimal problems including multi-step operations, word problems, and real-world applications.

Question 1: Sarah ran 2.45 miles on Monday and 3.78 miles on Tuesday. How far did she run in total?

Answer: 6.23 miles

Steps:

  1. Add: 2.45 + 3.78
  2. Hundredths: 5 + 8 = 13 (write 3, carry 1)
  3. Tenths: 4 + 7 + 1 = 12 (write 2, carry 1)
  4. Ones: 2 + 3 + 1 = 6
  5. Answer: 6.23 miles

Question 2: A rope was 5.0 meters long. You cut off 2.65 meters. How much remains?

Answer: 2.35 meters

Steps:

  1. Subtract: 5.00 - 2.65
  2. Borrow: 4.10 - 2.65 becomes 4.100 - 2.65
  3. Hundredths: 10 - 5 = 5
  4. Tenths: 9 - 6 = 3
  5. Ones: 4 - 2 = 2
  6. Answer: 2.35 meters

Question 3: Write 0.75 as a fraction in simplest form.

Answer: 3/4

Steps:

  1. 0.75 = 75/100
  2. Find GCF of 75 and 100: 25
  3. 75÷25 = 3, 100÷25 = 4
  4. Answer: 3/4

Question 4: Order from greatest to least: 3.45, 3.5, 3.405

Answer: 3.5, 3.45, 3.405

Steps:

  1. Convert to hundredths: 3.50, 3.45, 3.405
  2. Compare: 3.50 > 3.45 > 3.405
  3. Answer: 3.5, 3.45, 3.405

Question 5: Calculate: 4.6 + 2.8 + 1.5

Answer: 8.9

Steps:

  1. Add: 4.6 + 2.8 = 7.4
  2. Then: 7.4 + 1.5 = 8.9
  3. Or add all tenths: 6+8+5 = 19 tenths = 1.9
  4. Add ones: 4+2+1+1 = 8
  5. Answer: 8.9

Question 6: You bought items for $3.45, $2.89, and $1.50. Total cost?

Answer: $7.84

Steps:

  1. Add: $3.45 + $2.89 + $1.50
  2. Cents: 45 + 89 = 134 ($1.34), + 50 = 184 ($1.84)
  3. Dollars: 3 + 2 + 1 + 1 (from cents) = 7
  4. Answer: $7.84

Question 7: A tank holds 10.0 liters. It has 3.75 liters. How much more can fit?

Answer: 6.25 liters

Steps:

  1. Subtract: 10.00 - 3.75
  2. Borrow: 9.100 - 3.75
  3. Hundredths: 10 - 5 = 5
  4. Tenths: 9 - 7 = 2
  5. Ones: 9 - 3 = 6
  6. Answer: 6.25 liters

Question 8: Compare and explain: Is 0.8 greater than, less than, or equal to 0.80?

Answer: Equal (=)

Steps:

  1. 0.8 = 8 tenths = 80 hundredths
  2. 0.80 = 80 hundredths
  3. Trailing zeros don't change value
  4. Answer: Equal

Question 9: Calculate: (1.5 + 2.3) - 1.8

Answer: 2.0 or 2

Steps:

  1. First add: 1.5 + 2.3 = 3.8
  2. Then subtract: 3.8 - 1.8 = 2.0
  3. Answer: 2.0 or 2

Question 10: A recipe needs 2.5 cups flour. You have 1.75 cups. How much more needed?

Answer: 0.75 cups

Steps:

  1. Subtract: 2.5 - 1.75
  2. Think: 2.50 - 1.75
  3. Borrow: 1.150 - 1.75 becomes 2.50 - 1.75
  4. Hundredths: 50 - 75 (need borrow) → 10 from tenths
  5. 150 - 75 = 75
  6. Answer: 0.75 cups

Question 11: Write the expanded form of 5.37

Answer: 5 + 0.3 + 0.07

Steps:

  1. 5 ones = 5
  2. 3 tenths = 0.3
  3. 7 hundredths = 0.07
  4. Answer: 5 + 0.3 + 0.07

Question 12: Which is closest to 1: 0.98, 1.02, or 0.89?

Answer: 0.98

Steps:

  1. Distance from 1: 0.98 → 0.02 away
  2. 1.02 → 0.02 away
  3. 0.89 → 0.11 away
  4. 0.98 and 1.02 are equally close, but 0.98 < 1
  5. Answer: 0.98 (or accept 1.02)

Question 13: Calculate: 6.25 - 2.8

Answer: 3.45

Steps:

  1. Write as: 6.25 - 2.80
  2. Hundredths: 5 - 0 = 5
  3. Tenths: 2 - 8 (borrow) → 12 - 8 = 4
  4. Ones: 5 - 2 = 3
  5. Answer: 3.45

Question 14: You walked 1.2 km, ran 0.85 km, then walked 0.6 km. Total distance?

Answer: 2.65 km

Steps:

  1. Add: 1.2 + 0.85 + 0.6
  2. Think: 1.20 + 0.85 + 0.60
  3. 1.20 + 0.85 = 2.05
  4. 2.05 + 0.60 = 2.65
  5. Answer: 2.65 km

Question 15: A board is 8.5 feet. You need 6.75 feet. How much extra will remain?

Answer: 1.75 feet

Steps:

  1. Subtract: 8.5 - 6.75
  2. Write as: 8.50 - 6.75
  3. Borrow: 7.150 - 6.75
  4. Hundredths: 50 - 75 (borrow) → 150 - 75 = 75
  5. Wait, let me recalculate properly
  6. 8.50 - 6.75: Hundredths: 0-5 (borrow) → 10-5=5
  7. Tenths: 4-7 (borrow) → 14-7=7
  8. Ones: 7-6=1
  9. Answer: 1.75 feet

Question 16: Round 3.67 to the nearest tenth.

Answer: 3.7

Steps:

  1. Look at hundredths place: 7
  2. 7 ≥ 5, so round up
  3. 6 tenths rounds up to 7 tenths
  4. Answer: 3.7

Question 17: Calculate: 10.0 - 7.86

Answer: 2.14

Steps:

  1. Subtract: 10.00 - 7.86
  2. Borrow twice: 9.10 becomes 9.100
  3. Borrow: 8.1010... let's be careful
  4. 10.00 - 7.86:
  5. Hundredths: 0-6 (borrow) → 10-6=4
  6. Tenths: 9-8=1 (after borrowing)
  7. Ones: 9-7=2
  8. Answer: 2.14

Question 18: Which decimal is exactly between 2.4 and 2.5?

Answer: 2.45

Steps:

  1. 2.4 = 2.40, 2.5 = 2.50
  2. Middle value: (2.40 + 2.50) ÷ 2
  3. Or count: 2.40, 2.45, 2.50
  4. Answer: 2.45

Question 19: A movie is 2.25 hours. You've watched 1.5 hours. Time remaining?

Answer: 0.75 hours (or 45 minutes)

Steps:

  1. Subtract: 2.25 - 1.5
  2. Write as: 2.25 - 1.50
  3. Hundredths: 5 - 0 = 5
  4. Tenths: 2 - 5 (borrow) → 12 - 5 = 7
  5. Ones: 1 - 1 = 0
  6. Answer: 0.75 hours (45 minutes)

Question 20: Estimate and then calculate: 4.89 + 3.12 (Round to nearest whole first, then find exact)

Answer: Estimate: 8, Exact: 8.01

Steps:

  1. Estimate: 5 + 3 = 8
  2. Exact: 4.89 + 3.12
  3. Hundredths: 9 + 2 = 11 (write 1, carry 1)
  4. Tenths: 8 + 1 + 1 = 10 (write 0, carry 1)
  5. Ones: 4 + 3 + 1 = 8
  6. Answer: Estimate 8, Exact 8.01

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