Round the number 42.763 to 1 decimal place.
The Correct Answer and Explanation is:
To round the number 42.763 to one decimal place, we focus on the digit immediately to the right of the first decimal place, which is the second decimal place.
Steps for rounding:
- Identify the relevant digits: In the number 42.763, the digit in the first decimal place is 7 (the first digit after the decimal point), and the digit in the second decimal place is 6 (the second digit after the decimal point).
- Apply the rounding rule: The rounding rule states that if the digit to be dropped (the second decimal place, in this case, 6) is 5 or greater, we round up the first decimal place by 1. If the digit is less than 5, we simply keep the first decimal place as it is.
- Perform the rounding: Since the second decimal place digit (6) is greater than 5, we add 1 to the first decimal place digit:
- First decimal place: 7
- Adding 1 gives us 8.
- Construct the final rounded number: Thus, when rounded to one decimal place, 42.763 becomes 42.8.
Therefore, the final answer is 42.8.
Explanation of Rounding
Rounding is a mathematical technique used to reduce the number of significant digits in a number while keeping its value as close as possible to the original. It is particularly useful in various fields such as finance, science, and engineering, where precise measurements are often approximated for ease of communication and calculation.
When rounding to a specific number of decimal places, it’s crucial to identify which digit is being considered for rounding and to understand how the digit immediately following it will affect the rounding outcome. This is often encapsulated in the “5-and-up round up” rule, which simplifies numerical representation while maintaining accuracy.
In this case, rounding to one decimal place (the tenths position) allows us to convey the essential information of the number without unnecessary complexity. This practice is not only applicable to decimal numbers but can also be extended to whole numbers, currencies, and measurements in order to facilitate easier interpretation and communication. Overall, rounding serves as a fundamental mathematical skill that enhances clarity and precision in numerical expressions.