Round the following numbers as indicated
To the nearest thousandth
A. 687524
B. 41.86632
The correct answer and explanation is :
To the nearest thousandth
A. 687524
The number 687524 is a whole number, meaning it has no decimal part. When rounding to the nearest thousandth, you only look at the first three digits after the decimal point. Since 687524 has no decimal point, rounding to the nearest thousandth results in 687524.000.
B. 41.86632
To round this number to the nearest thousandth, we focus on the fourth digit after the decimal point, which is 3. According to rounding rules, if the digit in the thousandths place (third digit after the decimal) is followed by a number that is 5 or greater, we round up. If it’s less than 5, we round down.
Here’s the breakdown:
- The number is 41.86632.
- The thousandths place (third digit after the decimal) is 6.
- The next digit, which is in the ten-thousandths place, is 3.
- Since the digit after the thousandths place (which is 3) is less than 5, we leave the thousandths place unchanged.
Thus, rounding 41.86632 to the nearest thousandth results in 41.866.
Explanation of Rounding
Rounding is a mathematical process used to simplify numbers, making them easier to work with while maintaining a reasonable degree of accuracy. When rounding to the nearest thousandth, we focus on the first three digits after the decimal point.
- Identifying the Decimal Places: The digit in the thousandths place is the third digit after the decimal point. For example, in 41.86632, the digit 6 is in the thousandths place.
- Rounding Rules: If the digit immediately after the place you’re rounding to is 5 or greater, you round the target digit up by one. If it’s less than 5, you leave the target digit unchanged and discard the remaining digits.
- Application to Whole Numbers: Whole numbers like 687524 have no digits after the decimal point. So, when rounding them to the nearest thousandth, you add “.000” to indicate that the number has been rounded to three decimal places.
Rounding ensures consistency, particularly when working with measurements, data analysis, or financial calculations, where precision is necessary but not always practical to maintain to many decimal places.