Currency Exchange

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Answer Key & Explanations

Currency Exchange · Grade 8 · Worksheet 2

1. Liam is exchanging 450 US dollars for euros. The exchange rate is $1 = 0.85€. How many euros will he receive? Answer: 382.5 Solution: Identify the given values: amount in US dollars = 450, exchange rate = 0.85 euros per dollar. Multiply the amount in dollars by the exchange rate: 450 × 0.85.
   Full step-by-step solution

   Step 1: Identify the given values: amount in US dollars = 450, exchange rate = 0.85 euros per dollar. Step 2: Multiply the amount in dollars by the exchange rate: 450 × 0.85. Step 3: Calculate: 450 × 0.85 = 450 × (85/100) = (450 × 85) / 100 = 38250 / 100 = 382.5. Step 4: Liam will receive 382.5 euros. The answer is 382.5.

2. Liam is exchanging 375 Canadian dollars (CAD) to US dollars (USD). The exchange rate is 1 CAD = 0.73 USD. How many US dollars will he receive? Answer: 273.75 Solution: Identify the amount in CAD: 375 CAD. Identify the exchange rate: 1 CAD = 0.73 USD. Multiply the CAD amount by the rate: 375 × 0.73.
   Full step-by-step solution

   Step 1: Identify the amount in CAD: 375 CAD. Step 2: Identify the exchange rate: 1 CAD = 0.73 USD. Step 3: Multiply the CAD amount by the rate: 375 × 0.73. Step 4: 375 × 0.73 = 375 × (73/100) = (375 × 73) / 100. Step 5: 375 × 73 = 375 × 70 + 375 × 3 = 26250 + 1125 = 27375. Step 6: Divide by 100: 27375 / 100 = 273.75. The answer is 273.75 USD.

3. Liam has 375 Canadian dollars and wants to convert them to US dollars. The exchange rate is 1 CAD = 0.73 USD. How many US dollars will Liam receive? Answer: 273.75 Solution: Identify the amount in Canadian dollars: 375 CAD. Identify the exchange rate: 1 CAD = 0.73 USD. Multiply: 375 × 0.73 = 375 × (73/100) = (375 × 73) / 100.
   Full step-by-step solution

   Step 1: Identify the amount in Canadian dollars: 375 CAD. Step 2: Identify the exchange rate: 1 CAD = 0.73 USD. Step 3: Multiply: 375 × 0.73 = 375 × (73/100) = (375 × 73) / 100. Step 4: 375 × 73 = 375 × 70 + 375 × 3 = 26250 + 1125 = 27375. Step 5: Divide by 100: 27375 / 100 = 273.75. The answer is 273.75 USD.

4. (4 × 10³) × (2.5 × 10⁴) = ? Answer: 100000000 Solution: Multiply the coefficients: 4 × 2.5 = 10 Add the exponents: 3 + 4 = 7 Combine the results: 10 × 10⁷ Convert to standard form: 10 × 10,000,000 = 100,000,000 The answer is 100000000.
   Full step-by-step solution

   Step 1: Multiply the coefficients: 4 × 2.5 = 10 Step 2: Add the exponents: 3 + 4 = 7 Step 3: Combine the results: 10 × 10⁷ Step 4: Convert to standard form: 10 × 10,000,000 = 100,000,000 The answer is 100000000.

5. A rectangular solar panel has dimensions of 3.6 × 10³ millimeters by 2.4 × 10² millimeters. What is the area of the solar panel in square millimeters? Express your answer in scientific notation. Answer: 8.64×10^5 Solution: Step 1: Write the area formula: Area = length × width Step 2: Substitute the given values: Area = (3.6 × 10³) × (2.4 × 10²) Step 3: Multiply the coefficients: 3.6 × 2.4 = 8.64 Step 4: Add the exponents: 10³ × 10² = 10^(3+2) = 10^5 Step 5: Combine the results: 8.64 × 10^5 Step 6: Verify the…
   Full step-by-step solution

   Step 1: Write the area formula: Area = length × width Step 2: Substitute the given values: Area = (3.6 × 10³) × (2.4 × 10²) Step 3: Multiply the coefficients: 3.6 × 2.4 = 8.64 Step 4: Add the exponents: 10³ × 10² = 10^(3+2) = 10^5 Step 5: Combine the results: 8.64 × 10^5 Step 6: Verify the coefficient is between 1 and 10 (8.64 is valid) The area of the solar panel is 8.64 × 10^5 square millimeters.

6. Sophia has 126 US dollars and wants to convert them to euros. The exchange rate is 1 US dollar = 0.86 euros. How many euros will she receive? Answer: 108.36 Solution: Identify the amount in US dollars: 126 dollars. Identify the exchange rate: 1 dollar = 0.86 euros. Multiply: 126 × 0.86 = 108.36.
   Full step-by-step solution

   Step 1: Identify the amount in US dollars: 126 dollars. Step 2: Identify the exchange rate: 1 dollar = 0.86 euros. Step 3: Multiply: 126 × 0.86 = 108.36. Step 4: Sophia will receive 108.36 euros. The answer is 108.36.

7. 5² + √(81) - 2³ = ? Answer: 26 Solution: 5² + √(81) - 2³ Calculate 5². 5² means 5 × 5 = 25. Calculate √(81).
   Full step-by-step solution

   Let's solve step by step. We have: 5² + √(81) - 2³ Step 1: Calculate 5². 5² means 5 × 5 = 25. Step 2: Calculate √(81). The square root of 81 is 9, because 9 × 9 = 81. Step 3: Calculate 2³. 2³ means 2 × 2 × 2 = 8. Step 4: Substitute these values into the expression: 25 + 9 - 8 Step 5: Perform the addition first: 25 + 9 = 34 Step 6: Then subtract 8: 34 - 8 = 26 Final answer: 26

8. Noah is exchanging 616 US dollars (USD) to Canadian dollars (CAD). The exchange rate is 1 USD = 1.36 CAD. How many Canadian dollars will Noah receive? Answer: 837.76 Solution: Identify the given information. Noah has 616 USD. The exchange rate is 1 USD = 1.36 CAD.
   Full step-by-step solution

   Step 1: Identify the given information. Noah has 616 USD. The exchange rate is 1 USD = 1.36 CAD. Step 2: To convert USD to CAD, multiply the number of USD by the exchange rate (CAD per USD). Step 3: Calculate: 616 × 1.36 Step 4: First, multiply 616 by 1: 616 × 1 = 616 Step 5: Then, multiply 616 by 0.36: 616 × 0.36 = 616 × (36/100) = (616 × 36) / 100 = 22176 / 100 = 221.76 Step 6: Add the two parts: 616 + 221.76 = 837.76 Step 7: Therefore, Noah will receive 837.76 CAD. The answer is 837.76.

9. (3.6 × 10⁸) ÷ (9 × 10³) = ? Answer: 40000 Solution: Separate the coefficients and powers of 10: (3.6 ÷ 9) × (10⁸ ÷ 10³) Divide the coefficients: 3.6 ÷ 9 = 0.4 Apply the exponent rule for division: 10⁸ ÷ 10³ = 10^(8-3) = 10⁵ Multiply the results: 0.4 × 10⁵ = 0.4 × 100,000 = 40,000 The answer is 40000.
   Full step-by-step solution

   Step 1: Separate the coefficients and powers of 10: (3.6 ÷ 9) × (10⁸ ÷ 10³) Step 2: Divide the coefficients: 3.6 ÷ 9 = 0.4 Step 3: Apply the exponent rule for division: 10⁸ ÷ 10³ = 10^(8-3) = 10⁵ Step 4: Multiply the results: 0.4 × 10⁵ = 0.4 × 100,000 = 40,000 The answer is 40000.