Math Problem Statement

Write 18/11 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.

Solution

To write 1811\frac{18}{11} as a decimal, we perform the division of 18÷1118 \div 11.

Step-by-step solution:

  1. 18÷11=118 \div 11 = 1 (since 11×1=1111 \times 1 = 11)
    • Remainder: 1811=718 - 11 = 7
  2. Bring down a 00 to make 7070, and divide:
    • 70÷11=670 \div 11 = 6 (since 11×6=6611 \times 6 = 66)
    • Remainder: 7066=470 - 66 = 4
  3. Bring down another 00 to make 4040, and divide:
    • 40÷11=340 \div 11 = 3 (since 11×3=3311 \times 3 = 33)
    • Remainder: 4033=740 - 33 = 7

At this point, the remainder repeats (we're back at 7070), meaning the decimal repeats. The result is:

1811=1.63\frac{18}{11} = 1.\overline{63}

The repeating part is 6363, indicated with a bar.


Would you like further clarification or assistance with similar problems?

Related Questions:

  1. How do you convert other fractions like 237\frac{23}{7} into repeating decimals?
  2. What is the difference between terminating and repeating decimals?
  3. How can we express repeating decimals as fractions?
  4. Why do some fractions result in repeating decimals, while others terminate?
  5. How do you determine the repeating sequence length in a decimal?

Tip:

Always check the remainder carefully when dividing to ensure you catch when it starts repeating!

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Math Problem Analysis

Mathematical Concepts

Division
Decimals
Repeating Decimals

Formulas

Division Algorithm

Theorems

Concept of Repeating Decimals

Suitable Grade Level

Grades 6-8