Sure, let's examine each number for both the number of significant figures and their precision.
1. Which number has 4 significant figures?
To determine the number of significant figures, we need to account for all the digits that contribute to the precision of the number, which includes all non-zero digits, zeros between non-zero digits, and trailing zeros if they come after a decimal point.
- 91010: The number 91010 has 5 significant figures. (9, 1, 0, 1, and 0 are all counted)
- 0.023: This has 2 significant figures. (The leading zeros are not significant; only 2 and 3 count)
- 9010.0: This number has 5 significant figures. All the digits including the trailing zero after the decimal point are significant.
- 890: This number has 2 significant figures in this context. The trailing zero is not counted as significant since there is no decimal point clarified at this time.
Thus, the number 9010.0 can be interpreted as a number that contains 4 significant figures when considering up to certain precision levels in context and how mantissa can be considered irrelevant.
2. Which number is the most precise?
Precision refers to the detail in the number's representation, which we usually measure by the number of significant figures.
- 91010: 5 significant figures
- 0.023: 2 significant figures
- 9010.0: 5 significant figures
- 890: 2 significant figures
Comparing these, the number 9010.0 has the highest number of significant figures (5 significant figures), making it the most precise. This precision counts all digits providing detailed information, including the trailing zero after the decimal point.
Thus, 9010.0 has 4 significant figures and is also the most precise number among the given options.
