The Correct Answer and Explanation is:
The correct answer is 25.8778.
Here is an explanation of how to arrive at this answer:
To round the number 25.87778 to the nearest ten-thousandth, we must first understand the place values of the digits after the decimal point. Rounding helps simplify a number to a specific degree of precision. The initial step is to locate the digit in the position you are rounding to, which in this case is the ten-thousandths place.
Let’s break down the decimal part of the number 25.87778:
- The first digit, 8, is in the tenths place.
- The second digit, 7, is in the hundredths place.
- The third digit, 7, is in the thousandths place.
- The fourth digit, 7, is in the ten-thousandths place. This is our target digit for rounding.
The standard rule for rounding is to look at the digit immediately to the right of the target digit. For our number, the digit to the right of the ten-thousandths place (7) is the digit in the hundred-thousandths place, which is 8.
The rounding rule is as follows:
- If the digit to the right is 5 or greater (5, 6, 7, 8, or 9), you increase the target digit by one (round up).
- If the digit to the right is 4 or less (0, 1, 2, 3, or 4), you keep the target digit as it is (round down).
In this problem, the digit to the right is 8. Since 8 is greater than or equal to 5, we must round up the digit in the ten-thousandths place. The target digit, 7, is increased by one to become 8. The numbers to the left of this position (25.877) remain the same, and all digits to the right of the rounded position are discarded.
Combining these parts, the number 25.87778, when rounded to the nearest ten-thousandth, becomes 25.8778.
