Sure, let's solve each of these problems step-by-step while paying close attention to significant digits.
### Problem 1: [tex]\( 15.87 \text{ g} - 1.200 \text{ g} \)[/tex]
1. Subtract the numbers:
[tex]\[
15.87 \text{ g} - 1.200 \text{ g} = 14.670 \text{ g}
\][/tex]
2. Determine the number of significant digits:
- [tex]\( 15.87 \text{ g} \)[/tex] has 4 significant digits.
- [tex]\( 1.200 \text{ g} \)[/tex] has 4 significant digits.
- The result should be rounded to the smallest number of decimal places, which is 3 decimal places from 1.200 g.
3. Round the result to 3 decimal places:
[tex]\[
14.670 \text{ g} \rightarrow 14.670 \text{ g}
\][/tex]
So, [tex]\( 15.87 \text{ g} - 1.200 \text{ g} = 14.670 \text{ g} \)[/tex].
### Problem 2: [tex]\( 15.77 \text{ g} - 0.900 \text{ g} \)[/tex]
1. Subtract the numbers:
[tex]\[
15.77 \text{ g} - 0.900 \text{ g} = 14.870 \text{ g}
\][/tex]
2. Determine the number of significant digits:
- [tex]\( 15.77 \text{ g} \)[/tex] has 4 significant digits.
- [tex]\( 0.900 \text{ g} \)[/tex] has 4 significant digits.
- The result should be rounded to the smallest number of decimal places, which is 3 decimal places from 0.900 g.
3. Round the result to 3 decimal places:
[tex]\[
14.870 \text{ g} \rightarrow 14.870 \text{ g}
\][/tex]
So, [tex]\( 15.77 \text{ g} - 0.900 \text{ g} = 14.870 \text{ g} \)[/tex].
### Problem 3: [tex]\( 15.500 \text{ g} + 1.1 \text{ g} \)[/tex]
1. Add the numbers:
[tex]\[
15.500 \text{ g} + 1.1 \text{ g} = 16.600 \text{ g}
\][/tex]
2. Determine the number of significant digits:
- [tex]\( 15.500 \text{ g} \)[/tex] has 4 significant digits.
- [tex]\( 1.1 \text{ g} \)[/tex] has 2 significant digits.
- The result should be rounded to the smallest number of decimal places, which is 1 decimal place from 1.1 g.
3. Round the result to 1 decimal place:
[tex]\[
16.600 \text{ g} \rightarrow 16.6 \text{ g}
\][/tex]
So, [tex]\( 15.500 \text{ g} + 1.1 \text{ g} = 16.6 \text{ g} \)[/tex].
The final results with the correct significant digits are:
[tex]\[
\begin{array}{l}
15.87 \text{ g} - 1.200 \text{ g} = 14.67 \text{ g} \\
15.77 \text{ g} - 0.900 \text{ g} = 14.87 \text{ g} \\
15.500 \text{ g} + 1.1 \text{ g} = 16.6 \text{ g}
\end{array}
\][/tex]
