Convert 11/16 to a decimal number and round the result to the nearest thousandths. 0.6875
The Correct Answer and Explanation is:
To convert the fraction 11/16 into a decimal, divide the numerator by the denominator. Performing the division:
11 ÷ 16 = 0.6875
This result must be rounded to the nearest thousandths. The thousandths place is the third digit after the decimal point. In the number 0.6875, the digit in the thousandths place is 7, and the digit immediately after it, in the ten-thousandths place, is 5. When rounding, the rule states that if the digit following the rounding place is 5 or greater, the number should be rounded up. Since 5 meets this criterion, the 7 in the thousandths place must increase by one, transforming it into 8. The digits before it remain unchanged, leading to the final rounded value:
0.688
This process is rooted in standard rounding principles used in mathematics to simplify numerical representations while maintaining accuracy within the given level of precision. Rounding to the nearest thousandths is particularly useful in applications where approximate values are sufficient, such as scientific measurements, financial calculations, or statistical analysis.
Fraction-to-decimal conversion serves practical purposes in various fields. In engineering, fractions often appear in measurements, and converting them into decimals helps streamline calculations. In chemistry, precise decimal values assist in expressing concentrations or molecular ratios with clarity. Additionally, computer programming benefits from decimal approximations when designing algorithms that rely on floating-point operations.
Understanding how to perform division-based conversions and proper rounding techniques enables accurate representation of numerical data across different domains. This skill supports problem-solving in academic and professional contexts, ensuring efficiency in handling measurements and computations. Whether determining financial estimates, scientific constants, or industrial specifications, rounding provides a structured approach for expressing numbers with appropriate precision. In this specific case, rounding 0.6875 to the nearest thousandths results in the final answer:
0.688
