The Correct Answer and Explanation is:
The correct answer is (C) 5.39.
Rounding is a mathematical process used to simplify a number to a certain place value, making it easier to work with while keeping its value close to the original. The process involves deciding whether to keep a digit the same or increase it based on the value of the digit that follows. To round the number 5.389 to the nearest hundredth, we must follow a specific set of rules based on place value.
First, it is essential to identify the place values in the number 5.389. The digit 5 is in the ones place, which is to the left of the decimal point. To the right of the decimal, the 3 is in the tenths place, the 8 is in the hundredths place, and the 9 is in the thousandths place. Our goal is to round to the hundredths place, so our target digit is the 8. This is the digit that will either stay the same or be increased by one.
The next step is to look at the digit immediately to the right of our target digit. This is often called the “deciding” digit. In this case, that is the 9 in the thousandths place. The fundamental rule of rounding is: if the deciding digit is 5 or greater, which includes 5, 6, 7, 8, or 9, we round up the target digit. If the deciding digit is 4 or less, which includes 0, 1, 2, 3, or 4, we keep the target digit as it is.
Since the deciding digit here is 9, and 9 is greater than 5, we must round up the digit in the hundredths place. The target digit, 8, when rounded up by one, becomes 9. The digits to the left of the hundredths place, which are 5.3, remain unchanged. After rounding, all digits to the right of the hundredths place are dropped. Combining these parts gives us the final rounded number: 5.39.
Let’s consider why the other options are incorrect. Option (A) 5.4 is the result of rounding 5.389 to the nearest tenth, not the hundredth. Option (B) 5.38 would be the answer if we were to round down or truncate, which is incorrect because the deciding digit, 9, requires us to round up. Option (D) 5.399 has not been rounded to the hundredth place at all. Thus, 5.39 is the only correctly rounded number.
