Math Problem Statement

Work out the first six digits after the decimal point when 7/11 is written as a decimal. Write a sentence to explain what you notice about your answer.

Solution

To solve 711\frac{7}{11} as a decimal, let's divide 7 by 11.

Performing the division:

7÷11=0.6363637 \div 11 = 0.636363\ldots

The decimal form of 711\frac{7}{11} is a repeating decimal: 0.630.\overline{63}.

So, the first six digits after the decimal point are 0.636363.

Noticing about the answer:

The digits 63 repeat continuously, which makes the decimal representation of 711\frac{7}{11} a repeating decimal.

Do you want more details or have any questions?

Here are some related questions you can explore:

  1. Why do some fractions result in repeating decimals?
  2. What is the difference between terminating and repeating decimals?
  3. How can you identify a repeating decimal pattern more quickly?
  4. What happens if you multiply a repeating decimal like 0.630.\overline{63} by 11?
  5. How does long division help in determining repeating decimals?

Tip: When dividing two numbers and the division doesn't end after a few decimal places, the result may be a repeating decimal.

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Math Problem Analysis

Mathematical Concepts

Fractions
Decimals
Repeating Decimals

Formulas

Long Division

Theorems

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Suitable Grade Level

Grades 5-7