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Measurement and Matter

Counting significant digits when measurements are added or subtracted

Add or subtract the following measurements. Be sure each answer you enter contains the correct number of significant digits.

[tex]\[
\begin{array}{l}
15.87\, \text{g} - 1.200\, \text{g} = \square\, \text{g} \\
15.77\, \text{g} - 0.900\, \text{g} = \square\, \text{g} \\
15.500\, \text{g} + 1.1\, \text{g} = \square\, \text{g}
\end{array}
\][/tex]



Answer :

GinnyAnswer
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]

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