Math Problem Statement

1/11= show me step by step

Solution

To solve 111\frac{1}{11} as a decimal, here's the step-by-step division process:

Step 1: Set up the division

We are dividing 1 by 11, so:

1÷111 \div 11

Step 2: Add decimal points and zeroes

Since 1 is smaller than 11, we start by adding a decimal point to 1, making it 1.000000 (adding zeroes as needed).

So now we're dividing 1.000000 by 11.

Step 3: Perform long division

  1. 11 into 1: It goes 0 times. 0.0.

  2. 11 into 10: It goes 0 times again. 0.00.0

  3. 11 into 100: It goes 9 times (since 11×9=9911 \times 9 = 99). Write down 9, and subtract 99 from 100, leaving a remainder of 1. 0.090.09

  4. 11 into 10 (bring down the next 0): It goes 0 times again. 0.0900.090

  5. 11 into 100 (bring down another 0): It goes 9 times again (since 11×9=9911 \times 9 = 99). Subtract 99 from 100, leaving a remainder of 1 again. 0.09090.0909

This pattern will repeat indefinitely, so:

111=0.0909090909=0.09\frac{1}{11} = 0.0909090909\ldots = 0.\overline{09}

Thus, the decimal form of 111\frac{1}{11} is a repeating decimal 0.090.\overline{09}.


Would you like further details on how repeating decimals work, or do you have any other questions?

Related questions:

  1. How do you convert repeating decimals to fractions?
  2. What is the decimal representation of 17\frac{1}{7}?
  3. How can long division help with more complex fractions?
  4. Why do some fractions have repeating decimal expansions?
  5. What is the relationship between fractions and decimals?

Tip: Always double-check your remainder when performing long division to ensure accurate results!

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Math Problem Analysis

Mathematical Concepts

Fractions
Decimals
Long Division
Repeating Decimals

Formulas

Long Division for Fractions

Theorems

Repeating Decimal Theorem

Suitable Grade Level

Grades 5-7