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Magazine Chapter 7: Problem 92
Write as a decimal. $$\frac{3}{8}$$
Short Answer
Expert verified
The decimal representation of \( \frac{3}{8} \) is 0.375.
Step by step solution
01
Understand the Fraction
We are asked to convert the fraction \( \frac{3}{8} \) to a decimal. The fraction represents a division problem where 3 is divided by 8.
02
Set Up the Division
Write the division of 3 by 8. This requires placing 3 inside the division bracket (dividend) and 8 outside (divisor).
03
Perform the Division
Since 3 is smaller than 8, we need to add a decimal point and some zeros to 3, making it 3.000. We then check how many times 8 goes into 30 (which is 3), and find that it fits 0 times, so put 0 in the quotient beside the decimal point.
04
Continue the Division
Multiply 8 by 0 to get 0 and subtract from getting 30. Bring down the next 0 to make it 30. Now, check how many times 8 goes into 30, which is 3 times, as 8 times 3 equals 24.
05
Calculate Remainder
Subtract 24 from 30 to get 6. Bring down another 0 to make it 60. Determine how many times 8 goes into 60, which is 7, because 8 times 7 equals 56.
06
Calculate the Next Remainder
Subtract 56 from 60 to get 4. Bring down another 0 to make it 40. Determine how many times 8 goes into 40, which is 5, because 8 times 5 equals 40.
07
Complete the Division
Subtract 40 from 40 to get 0, completing the division process. Thus, the quotient is 0.375.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Division Process
To convert a fraction like \( \frac{3}{8} \) into a decimal, the first major step involves understanding the division process. The fraction \( \frac{3}{8} \) essentially means dividing 3 by 8. This division isn't straightforward, as 3 is smaller than 8.
Here's a step-by-step on how to carry out the division process:
Here's a step-by-step on how to carry out the division process:
- Place the number 3 inside the division bracket, which is known as the dividend.
- The number 8 acts as the divisor and is placed outside the bracket.
Decimal Representation
In obtaining the decimal representation of a fraction like \( \frac{3}{8} \), we follow the division process meticulously. The goal is to convert the division into a numeric decimal form that effectively expresses the fraction in a different way.
Let's break this down further:
Let's break this down further:
- Recognize that by performing the division, 8 doesn't go into 3, so we need a decimal and start adding zeros, turning 3 into 3.000.
- Divide 30 by 8, which fits 3 times, giving us 24. Hence, the initial part of our decimal is 0.3.
- The remainder (6) is not yet zero, indicating more division steps are necessary to find the next decimal places.
Step-by-Step Math Solutions
Offering step-by-step math solutions is crucial for problems like fraction to decimal conversions. A clear, detailed breakdown ensures that students not only find the right answer but also comprehend the procedures involved.
Here鈥檚 the reason why step-by-step solutions are beneficial:
Here鈥檚 the reason why step-by-step solutions are beneficial:
- They guide you through each phase, such as division setup, performing the division, and calculating remainders.
- By showcasing intermediary steps, students learn to avoid common pitfalls and develop problem-solving skills.
- When the solution says to "bring down another zero," it鈥檚 crucial for grasping why this results in extending the division to the decimal places required.
