Math Problem Statement

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Solution

The image shows the number 0.00560.0056 with a bar over the digits "56," indicating that these digits repeat indefinitely. This notation represents a repeating decimal, which can be written as:

0.0056=0.0056565656560.\overline{0056} = 0.005656565656\ldots

This repeating decimal can also be expressed as a fraction. Let me calculate that for you.

Let's denote x=0.0056x = 0.\overline{0056}. To convert this repeating decimal to a fraction:

  1. Multiply xx by 10000 to move the repeating part to the left of the decimal point: 10000x=56.005610000x = 56.\overline{0056}

  2. Subtract the original equation from this new equation: 10000xx=56.00560.005610000x - x = 56.\overline{0056} - 0.\overline{0056} 9999x=569999x = 56

  3. Solve for xx: x=569999x = \frac{56}{9999}

Thus, 0.00560.\overline{0056} as a fraction is 569999\frac{56}{9999}.

Would you like any further details or have any questions about this process?

Here are some related questions you might find interesting:

  1. How can you convert any repeating decimal to a fraction?
  2. What is the significance of repeating decimals in mathematics?
  3. How do you identify the repeating part of a decimal?
  4. Can repeating decimals be represented as terminating decimals?
  5. How can this fraction 569999\frac{56}{9999} be simplified further?

Tip: When dealing with repeating decimals, always consider the length of the repeating sequence to determine the appropriate power of 10 for multiplication.

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Math Problem Analysis

Mathematical Concepts

Decimal Representation
Repeating Decimals
Fraction Conversion

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12