Math Problem Statement
1/11= show me step by step
Solution
To solve as a decimal, here's the step-by-step division process:
Step 1: Set up the division
We are dividing 1 by 11, so:
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
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11 into 1: It goes 0 times.
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11 into 10: It goes 0 times again.
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11 into 100: It goes 9 times (since ). Write down 9, and subtract 99 from 100, leaving a remainder of 1.
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11 into 10 (bring down the next 0): It goes 0 times again.
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11 into 100 (bring down another 0): It goes 9 times again (since ). Subtract 99 from 100, leaving a remainder of 1 again.
This pattern will repeat indefinitely, so:
Thus, the decimal form of is a repeating decimal .
Would you like further details on how repeating decimals work, or do you have any other questions?
Related questions:
- How do you convert repeating decimals to fractions?
- What is the decimal representation of ?
- How can long division help with more complex fractions?
- Why do some fractions have repeating decimal expansions?
- 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