The Correct Answer and Explanation is:
The correct answer is 9778.
To round the number 9777.81034 to the nearest whole number, we must follow a systematic process that determines which whole number is closest in value. A whole number is an integer without any fractional or decimal parts. The task is to decide if 9777.81034 is closer to 9777 or to 9778.
The key to this process lies in examining the digit immediately to the right of the place value we are rounding to. In this problem, we are rounding to the nearest whole number, which means our focus is on the ones place. The digit currently in the ones place is the final 7 in 9777. The digit directly to its right, which is located in the tenths place, is the one that will guide our decision. For the number 9777.81034, this critical digit is 8.
The universal rule for rounding is straightforward. If the digit you are looking at is 5 or greater (that is, 5, 6, 7, 8, or 9), you round up the digit in the place you are targeting. This means you increase the target digit by one. If the decision digit is 4 or less (that is, 4, 3, 2, 1, or 0), you round down, which means you leave the target digit as it is. This rule ensures we select the whole number that is mathematically nearest to the original decimal number.
In our specific example, the digit in the tenths place is 8. Since 8 falls into the category of ‘5 or greater’, the rule instructs us to round up. This means we must increase the digit in the ones place by one. The current digit in the ones place is 7. Adding one to 7 gives us 8.
Therefore, the whole number portion of our original number, 9777, is adjusted to become 9778. Once this adjustment is made, we discard all the digits that come after the decimal point. The result is that 9777.81034, when rounded to the nearest whole number, becomes 9778.
