Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

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]

Sagot :

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]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.