Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly 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]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.