What is this fraction in decimal form 3/8?
The Correct Answer and Explanation is:
To convert the fraction ( \frac{3}{8} ) into decimal form, we can use division. The numerator (3) is divided by the denominator (8). Here’s how the calculation unfolds step-by-step:
- Set up the division: We can express ( \frac{3}{8} ) as ( 3 \div 8 ).
- Perform the division:
- 8 does not go into 3, so we start with a 0 and place a decimal point, making it ( 3.0 ) (or ( 30 ) tenths).
- 8 goes into 30 three times (because ( 8 \times 3 = 24 )), leaving a remainder of 6 (since ( 30 – 24 = 6 )).
- Bring down a zero, making the new number 60.
- 8 goes into 60 seven times (as ( 8 \times 7 = 56 )), with a remainder of 4 (since ( 60 – 56 = 4 )).
- Bring down another zero, resulting in 40.
- 8 goes into 40 five times (because ( 8 \times 5 = 40 )), with no remainder (since ( 40 – 40 = 0 )).
Putting this all together, the division yields:
[
3 \div 8 = 0.375
]
Thus, the decimal representation of ( \frac{3}{8} ) is ( 0.375 ).
Explanation of the Conversion Process
The conversion of fractions to decimals is an essential skill in mathematics, especially in fields like science, engineering, and finance, where precise calculations are necessary. The process of converting ( \frac{3}{8} ) to a decimal not only illustrates basic arithmetic but also demonstrates the concept of division.
Understanding fractions and decimals is crucial because they are two different ways to represent parts of a whole. A fraction indicates a division of the numerator by the denominator, while a decimal expresses that division in a base-10 format, making it often easier to interpret and use in calculations. This conversion method helps facilitate comparisons and computations involving different measurements.
In real-world applications, such as cooking or financial transactions, having a decimal equivalent allows for greater precision and clarity. Therefore, learning how to convert fractions like ( \frac{3}{8} ) into decimals is a foundational skill that enhances numerical fluency and confidence in mathematical operations.