Answer :
Sure, let's express the number \( 367900 \) in standard form.
To convert a number to standard form, we express it as a product of a number between 1 and 10, and a power of 10.
Here are the step-by-step details:
1. Determine the significant figures:
Identify the digits of the number that are not zero and place the decimal point after the first significant digit. For \(367900\), the significant figures are \(3679\).
2. Place the decimal point:
We place the decimal point after the first digit \(3\). This gives us \(3.679\).
3. Count the number of places the decimal has moved:
The decimal point moved 5 places to the left (from after the zero to between 3 and 6).
4. Write the number as a product of this decimal and a power of 10:
We get \(3.679\), and the decimal has moved 5 places, so we multiply by \(10^5\).
Therefore, \(367900\) in standard form is
[tex]\[ 3.679 \times 10^5 \][/tex]
Next, let's identify the correct option from the given choices.
A. \(3.679 \times 10^4\)
B. \(3.679 \times 10^5\)
C. \(3.679 \times 10^6\)
D. \(3.679 \times 10^7\)
E. \(3.679 \times 10^8\)
Comparing our result \(3.679 \times 10^5\) with the options, we find that option B is correct.
So, the correct answer is:
[tex]\[ \boxed{3.679 \times 10^5} \][/tex]
and the corresponding option is:
[tex]\[ \boxed{B} \][/tex]
To convert a number to standard form, we express it as a product of a number between 1 and 10, and a power of 10.
Here are the step-by-step details:
1. Determine the significant figures:
Identify the digits of the number that are not zero and place the decimal point after the first significant digit. For \(367900\), the significant figures are \(3679\).
2. Place the decimal point:
We place the decimal point after the first digit \(3\). This gives us \(3.679\).
3. Count the number of places the decimal has moved:
The decimal point moved 5 places to the left (from after the zero to between 3 and 6).
4. Write the number as a product of this decimal and a power of 10:
We get \(3.679\), and the decimal has moved 5 places, so we multiply by \(10^5\).
Therefore, \(367900\) in standard form is
[tex]\[ 3.679 \times 10^5 \][/tex]
Next, let's identify the correct option from the given choices.
A. \(3.679 \times 10^4\)
B. \(3.679 \times 10^5\)
C. \(3.679 \times 10^6\)
D. \(3.679 \times 10^7\)
E. \(3.679 \times 10^8\)
Comparing our result \(3.679 \times 10^5\) with the options, we find that option B is correct.
So, the correct answer is:
[tex]\[ \boxed{3.679 \times 10^5} \][/tex]
and the corresponding option is:
[tex]\[ \boxed{B} \][/tex]
