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Magazine Chapter 6: Problem 47
Convert to decimal notation. \(\frac{25}{11}\)
Short Answer
Expert verified
The decimal notation of \(\frac{25}{11}\) is 2.27 with 27 repeating.
Step by step solution
01
- Understanding the fraction
Begin with the fraction \(\frac{25}{11}\). This fraction represents the division of 25 by 11.
02
- Perform the division
Divide 25 by 11 using long division. The quotient will give the decimal form.
03
- Long division process
First, 11 goes into 25 two times (2). Write down 2. Multiply 2 by 11 to get 22. Subtract 22 from 25 to get the remainder 3.
04
- Continue the division
Bring down a 0 to make the remainder 30. 11 goes into 30 two times (2). Write down 2 next to the 2. Multiply 2 by 11 to get 22. Subtract 22 from 30 to get the remainder 8.
05
- Repeat the process
Bring down another 0 to make the remainder 80. 11 goes into 80 seven times (7). Write down 7 next to the previous digits. Multiply 7 by 11 to get 77. Subtract 77 from 80 to get the remainder 3.
06
- Recognize the repeating decimal
Notice the remainder is now 3 again, just like in Step 3. This means the decimal form repeats. The repeating sequence is 27.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
long division
Long division is a method for dividing two numbers to obtain a quotient and a remainder. This technique helps break down complex division problems into simpler steps. To convert a fraction, like \(\frac{25}{11}\), to a decimal, you need to divide the numerator by the denominator using long division.
If the numerator is smaller than the denominator, append a decimal point to your quotient and add zeros to the numerator.
For example, dividing 25 by 11 goes like this:
If the numerator is smaller than the denominator, append a decimal point to your quotient and add zeros to the numerator.
For example, dividing 25 by 11 goes like this:
- 11 goes into 25 two times (since 2 * 11 = 22).
- Write 2 in the quotient and subtract 22 from 25 to get a remainder of 3.
- Bring down a 0 to make 30 and repeat the division.
repeating decimals
Repeating decimals are decimals in which one or more digits repeat infinitely. For example, when you divide 25 by 11, you get a quotient of 2.272727..., where 27 is the repeating sequence.
To identify repeating patterns:
To identify repeating patterns:
- Perform long division.
- Look for remainders that repeat.
- When a remainder repeats, the same sequence of digits in the quotient will repeat.
fraction to decimal conversion
Converting a fraction to a decimal involves dividing the numerator (the number above the line) by the denominator (the number below the line). For example, \(\frac{25}{11}\) can be converted to a decimal by performing the division 25 梅 11.
Here鈥檚 the step-by-step process:
Here鈥檚 the step-by-step process:
- Set up for long division by placing 25 inside the division bracket and 11 outside.
- Determine how many times 11 fits into the initial digit(s) of 25.
- Write the whole number result (quotient) above the division bracket.
- Subtract the product of 11 and the quotient from 25.
- Bring down the next digit to continue the process.
mathematics problem-solving
Mathematics problem-solving is the process of finding solutions to mathematical questions or problems. Here鈥檚 how you can approach problems like converting fractions to decimals:
- **Understand the problem:** Identify what is being asked. In our example, we need to convert \(\frac{25}{11}\) to a decimal.
- **Choose a strategy:** Decide the best method to solve the problem, such as long division for conversion.
- **Execute the plan:** Perform the calculations step-by-step, ensuring you follow each procedure correctly.
- **Review the process and solution:** Check if the result makes sense and identify any repeating decimals.
