Certainly! Let's solve the problem step-by-step:
### Step 1: Identify the numbers and their significant figures
We have two numbers we need to multiply:
[tex]\[ 0.14 \][/tex]
[tex]\[ 6.02 \times 10^{23} \][/tex]
- The number 0.14 has 2 significant figures.
- The number [tex]\( 6.02 \times 10^{23} \)[/tex] has 3 significant figures.
### Step 2: Perform the multiplication
We need to multiply these two numbers:
[tex]\[ 0.14 \times 6.02 \times 10^{23} \][/tex]
First, multiply the decimal numbers:
[tex]\[ 0.14 \times 6.02 = 0.8428 \][/tex]
Then, combine this result with the power of 10:
[tex]\[ 0.8428 \times 10^{23} = 8.428 \times 10^{22} \][/tex]
### Step 3: Determine the significant figures for the result
The result of a multiplication should be expressed with the same number of significant figures as the factor with the fewest significant figures. Among our numbers:
- 0.14 has 2 significant figures
- 6.02 has 3 significant figures
Therefore, our result should be rounded to 2 significant figures.
### Step 4: Round the result to the correct number of significant figures
The unrounded result is [tex]\( 8.428 \times 10^{22} \)[/tex]. Rounding this to 2 significant figures:
- The first digit is 8, and the second digit is 4.
- Looking at the third digit (2) which is less than 5, we do not round up.
So, [tex]\( 8.428 \times 10^{22} \)[/tex] rounded to 2 significant figures is [tex]\( 8.4 \times 10^{22} \)[/tex].
### Step 5: Present the final result
Thus, the result of [tex]\( 0.14 \times \left(6.02 \times 10^{23}\right) \)[/tex] is:
[tex]\[ 8.4 \times 10^{22} \][/tex]
To summarize:
- The exact result before rounding: [tex]\( 8.428 \times 10^{22} \)[/tex]
- The rounded result with correct significant figures: [tex]\( 8.4 \times 10^{22} \)[/tex]
- The number of significant figures in the final answer: 2
