supervisor: “Last week, you spoke with 800 customers in 40 hours

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supervisor: “Last week, you spoke with 800 customers in 40 hours.” employee: “That is an average of customers every 30 minutes.”

A. 5
B. 10
C. 15
D. 20
E. 25

how do you write 0.3 repeating as a fraction

    The Correct Answer and Explanation is:

    Question 1:

    Supervisor: “Last week, you spoke with 800 customers in 40 hours.”
    Employee: “That is an average of ____ customers every 30 minutes.”

    Step-by-step solution:

    • First, determine the number of 30-minute intervals in 40 hours.

    Since 1 hour = 60 minutes,
    40 hours = 40 × 60 = 2,400 minutes
    Each 30-minute interval = 30 minutes
    Number of 30-minute intervals = 2,400 ÷ 30 = 80

    • Now divide the total number of customers (800) by the number of 30-minute intervals (80):

    800 customers80 intervals=10 customers per 30 minutes\frac{800\ \text{customers}}{80\ \text{intervals}} = 10\ \text{customers per 30 minutes}

    ✅ Correct answer: B. 10

    Question 2:

    How do you write 0.3 repeating as a fraction?

    ✅ Correct answer: 1/3

    300-word Explanation:

    To convert 0.3 repeating (which is written as 0.3‾0.\overline{3}) to a fraction, follow a simple algebraic method:

    Let: x=0.3‾x = 0.\overline{3}

    This means that the decimal repeats indefinitely: x=0.3333…x = 0.3333\ldots

    Now, multiply both sides of the equation by 10: 10x=3.3333…10x = 3.3333\ldots

    Next, subtract the original equation from this new equation: 10x−x=3.3333…−0.3333…10x – x = 3.3333\ldots – 0.3333\ldots

    This gives: 9x=39x = 3

    Now solve for xx: x=39=13x = \frac{3}{9} = \frac{1}{3}

    So, 0.3‾=130.\overline{3} = \frac{1}{3}

    Why This Works:

    Repeating decimals are infinite, but they follow a consistent pattern. When the same digit repeats (like 3 in this case), we can isolate and remove the repetition by multiplying by powers of 10. By subtracting the two equations, the repeating parts cancel out, leaving a clean whole number that can be solved algebraically.

    This approach works for any repeating decimal. For example, 0.6‾=230.\overline{6} = \frac{2}{3}, and 0.1‾=190.\overline{1} = \frac{1}{9}. It’s an essential concept in mathematics because it shows how every repeating decimal has a fractional equivalent — proving that repeating decimals are rational numbers.

    Understanding how to convert repeating decimals into fractions is especially helpful in fields like nursing, science, and finance, where precise values and conversions are required.

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