Convert 250/3 to a decimal
The Correct Answer and Explanation is :
To convert the fraction ( \frac{250}{3} ) to a decimal, you can perform the division of the numerator (250) by the denominator (3).
Calculation:
- Division: When you divide 250 by 3, you can set it up like this:
- 3 goes into 25 (the first two digits of 250) eight times, because ( 3 \times 8 = 24 ).
- Subtract 24 from 25, which leaves you with 1.
- Bring down the next digit (0), making it 10.
- 3 goes into 10 three times, because ( 3 \times 3 = 9 ).
- Subtract 9 from 10, which leaves you with 1.
- Bring down another 0, making it 10 again.
- This process repeats, showing that the division will continue yielding 3 indefinitely.
The complete division can be expressed as:
[ 250 \div 3 = 83.3333\ldots ]
This is often rounded to ( 83.33 ) or expressed as ( 83.\overline{3} ), indicating that the digit 3 repeats indefinitely.
Explanation:
Converting a fraction to a decimal involves division. In this case, ( \frac{250}{3} ) illustrates how a whole number (250) is distributed over three parts. The decimal ( 83.33\ldots ) signifies that each of the three parts contains approximately 83.33 units. The repeating decimal indicates that there is no exact whole number representation for this division, as the original fraction is an example of an improper fraction where the numerator exceeds the denominator.
Understanding this conversion is crucial, especially in fields like mathematics, finance, and engineering, where precise calculations are necessary. Decimal representations are often easier to work with compared to fractions, particularly in calculations involving addition, subtraction, and comparison. Moreover, being familiar with repeating decimals is beneficial for grasping concepts in sequences and series, where limits and convergence are key considerations. Thus, ( \frac{250}{3} ) not only serves as a simple arithmetic exercise but also highlights essential mathematical principles.