To determine the digit and place value for the last significant digit of the number 1.4593 when rounding to three significant figures, we follow a detailed step-by-step process:
1. Identify the Significant Figures: Significant figures are the digits in a number that contribute to its precision. For the number 1.4593, all the digits (1, 4, 5, 9, 3) are significant because there are no leading zeros and no trailing zeros after a decimal point.
2. Round to Three Significant Figures: We need to round the number 1.4593 so that it retains only three significant figures. This involves the first three significant digits of the number, which are 1, 4, and 5.
3. Consider the Next Digit for Rounding: The fourth digit in the number is 9.
- According to rounding rules, if the next digit (the fourth one) is 5 or greater, we round the last digit we are keeping up by one.
4. Apply the Rounding Rule:
- The number becomes 1.46 because the next digit (9) is greater than 5.
- This changes the third significant digit from 5 to 6.
5. Determine the Last Significant Digit After Rounding:
- The rounded number to three significant figures is 1.46.
- The digits in 1.46 are 1 (ones place), 4 (tenths place), and 6 (hundredths place).
6. Identify the Last Significant Digit and Its Place Value:
- The last significant digit is 5 before the rounding, as it is responsible for the final rounded significant value.
- The place value of this digit before rounding was the hundredths place (0.01).
Therefore, the last significant digit before rounding to three significant figures is 5, and its place value is the hundredths place. This matches option A:
A. the 5 (the hundredths place)
