The Correct Answer and Explanation is:
The correct answer to the calculation shown in the image is 6.944… (the 4 repeats indefinitely), which can also be expressed as the exact fraction 125/18.
The image displays a division problem: 25,000 divided by 3,600. Solving this calculation involves determining how many times the divisor, 3,600, fits into the dividend, 25,000.
An effective first step to solve this is to simplify the numbers. Both 25,000 and 3,600 are large numbers that share a significant common factor. Since both numbers end with two zeros, they are both divisible by 100. Dividing the dividend and the divisor by 100 simplifies the problem without changing the outcome. This transforms the calculation into the much more manageable equation of 250 ÷ 36.
This simplified fraction, 250/36, can be reduced even further. Both the numerator (250) and the denominator (36) are even numbers, meaning they are divisible by 2. Dividing both by 2, we get the fraction 125/18. This is the fraction in its simplest form, as 125 and 18 do not share any other common factors. This exact fraction is a precise answer to the problem.
To express the answer as a decimal, we perform the division of 125 by 18. The result is not a finite number but a repeating decimal: 6.9444… . For practical use, this is often rounded to a specific number of decimal places, such as 6.94 when rounded to two places.
This particular calculation is quite common in fields like physics and engineering. For example, it is used when converting a speed from units per hour to units per second, because there are 3,600 seconds in an hour. Thus, a speed of 25,000 kilometers per hour is equivalent to approximately 6.94 kilometers per second.
