In which of the following pairs do both numbers contain the same number of significant figures? Check all that apply
37.0 m and 37.00 m
0.0810 m and 0.801 m
740.0 L and 7.4 * 10 ^ - 4 L
0.00053 s and 53000 s
37.0 m and 37.00 m
To determine which pairs have the same number of significant figures, we need to count the number of significant figures in each number.
37.0 m: This number has three significant figures.
37.00 m: This number also has three significant figures.
0.0810 m: This number has three significant figures.
0.801 m: This number has three significant figures.
740.0 L: This number has four significant figures.
7.4 * 10^-4 L: This number has two significant figures.
0.00053 s: This number has two significant figures.
53000 s: This number has three significant figures.
Based on the analysis, the pairs with the same number of significant figures are:
1. 37.0 m and 37.00 m
2. 0.0810 m and 0.801 m
Therefore, the correct pairs are:
37.0 m and 37.00 m
0.0810 m and 0.801 m
To determine which pairs of numbers contain the same number of significant figures, we need to count the significant figures in each number.
Significant figures in a number are digits that carry meaning and contribute to the precision of the measurement.
Let's analyze each pair of numbers:
1. 37.0 m and 37.00 m:
To count significant figures, we ignore leading and trailing zeros if they don't indicate a measurement's precision. In this case, both numbers have three significant figures because the zeros are between non-zero digits.
2. 0.0810 m and 0.801 m:
Again, we need to ignore leading zeros. In the first number, 0.0810 m, there are three significant figures because the zeros are between non-zero digits. In the second number, 0.801 m, there are only two significant figures because the zero at the end indicates a measurement precision of just two decimal places.
3. 740.0 L and 7.4 * 10^-4 L:
In the first number, 740.0 L, there are four significant figures because all the digits are non-zero, and the trailing zero indicates measurement precision. In the second number, 7.4 * 10^-4 L, the number written in scientific notation, only has two significant figures because the zeros before the 7 and after the 4 are not significant.
4. 0.00053 s and 53,000 s:
In the first number, 0.00053 s, there are two significant figures because the zeros are between non-zero digits. In the second number, 53,000 s, there are three significant figures because the zeros are significant when they're between non-zero digits.
After analyzing each pair, we can conclude that the pairs with the same number of significant figures are:
1. 37.0 m and 37.00 m (both have three significant figures)
2. 0.00053 s and 53,000 s (both have two significant figures)
Therefore, the correct pairs are 37.0 m and 37.00 m, as well as 0.00053 s and 53,000 s.