Answer :
To express the number 0.009402 in scientific notation, we need to convert it into a form that is represented as [tex]\(a \times 10^b\)[/tex], where [tex]\(1 \leq a < 10\)[/tex] and [tex]\(b\)[/tex] is an integer.
1. Identify the significant digits of the number:
The significant digits of the number 0.009402 are 9.402.
2. Determine where to place the decimal point to get a number between 1 and 10:
We need to move the decimal point in 0.009402 to the right until we get 9.402.
3. Count the number of places the decimal point is moved:
Moving the decimal point in 0.009402 three places to the right gives us 9.402.
4. Determine the exponent:
Since we moved the decimal point three places to the right to transform 0.009402 into 9.402, the exponent will be negative. Moving the decimal point to the right corresponds to multiplying by [tex]\(10^{-3}\)[/tex].
5. Combine the coefficient and the exponent:
Therefore, 0.009402 can be written in scientific notation as:
[tex]\[ 9.402 \times 10^{-3} \][/tex]
So, the correct expression in scientific notation is:
[tex]\[ \boxed{9.402 \times 10^{-3}} \][/tex]
Given the choices:
A. [tex]\(9.402 \times 10^{-6}\)[/tex]
B. [tex]\(9.402 \times 10^3\)[/tex]
C. [tex]\(9402 \times 10^6\)[/tex]
D. [tex]\(9.402 \times 10^{-3}\)[/tex]
The correct answer is D. [tex]\(9.402 \times 10^{-3}\)[/tex].
1. Identify the significant digits of the number:
The significant digits of the number 0.009402 are 9.402.
2. Determine where to place the decimal point to get a number between 1 and 10:
We need to move the decimal point in 0.009402 to the right until we get 9.402.
3. Count the number of places the decimal point is moved:
Moving the decimal point in 0.009402 three places to the right gives us 9.402.
4. Determine the exponent:
Since we moved the decimal point three places to the right to transform 0.009402 into 9.402, the exponent will be negative. Moving the decimal point to the right corresponds to multiplying by [tex]\(10^{-3}\)[/tex].
5. Combine the coefficient and the exponent:
Therefore, 0.009402 can be written in scientific notation as:
[tex]\[ 9.402 \times 10^{-3} \][/tex]
So, the correct expression in scientific notation is:
[tex]\[ \boxed{9.402 \times 10^{-3}} \][/tex]
Given the choices:
A. [tex]\(9.402 \times 10^{-6}\)[/tex]
B. [tex]\(9.402 \times 10^3\)[/tex]
C. [tex]\(9402 \times 10^6\)[/tex]
D. [tex]\(9.402 \times 10^{-3}\)[/tex]
The correct answer is D. [tex]\(9.402 \times 10^{-3}\)[/tex].
