convert this rational number to its decimal form and round to the nearest thousand 3/8?
The Correct Answer and Explanation is:
To convert the rational number 38\frac{3}{8}83 to its decimal form:38=0.375\frac{3}{8} = 0.37583=0.375
Rounding 0.375 to the nearest thousandth gives:0.375\boxed{0.375}0.375
Explanation:
A rational number is a number that can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero. In this case, 3 is the numerator, and 8 is the denominator.
To convert the fraction to a decimal, divide the numerator by the denominator. Dividing 3 by 8 produces 0.375 exactly. This value does not repeat or continue beyond the third decimal place, which indicates it is a terminating decimal.
The process of rounding to the nearest thousandth involves examining the fourth decimal place, if it exists, to determine whether the third digit should be rounded up or stay the same. In this case, the decimal 0.375 ends exactly at the third place, meaning there is no digit beyond the thousandth place. Therefore, no rounding is necessary, and the number remains 0.375.
This decimal form provides a useful representation, especially in cases where calculations, measurements, or comparisons are made more manageable using decimal numbers rather than fractions. For example, in practical applications such as engineering, banking, or data analysis, decimal representations often simplify operations and reduce errors.
Additionally, understanding decimal equivalents of fractions can enhance number sense and make it easier to estimate or work mentally with numerical data. In education, converting between fractions and decimals reinforces key concepts of division and place value.
Thus, the rational number 38\frac{3}{8}83 is exactly equal to 0.375 when written in decimal form, and rounding it to the nearest thousandth retains that same value.
