Certainly! Let's solve the given division problem step-by-step.
We need to evaluate the division of two numbers expressed in scientific notation:
[tex]\[ \frac{1.60 \times 10^{-4} \, \text{cm}^3}{6.0 \times 10^5 \, \text{cm}} \][/tex]
1. Separate the coefficients from the powers of 10:
The numerator is [tex]\( 1.60 \times 10^{-4} \)[/tex] and the denominator is [tex]\( 6.0 \times 10^5 \)[/tex].
2. Divide the coefficients:
[tex]\[
\frac{1.60}{6.0} = 0.2666666666666667
\][/tex]
3. Subtract the exponents of 10:
In scientific notation, when we divide powers of 10, we subtract the exponent in the denominator from the exponent in the numerator.
The exponent of the numerator is [tex]\(-4\)[/tex] and the exponent of the denominator is [tex]\(5\)[/tex]:
[tex]\[
10^{-4} \div 10^{5} = 10^{-4 - 5} = 10^{-9}
\][/tex]
4. Combine the results:
Combine the result of the coefficient [tex]\( 0.2666666666666667 \)[/tex] with the result of the powers of 10, [tex]\( 10^{-9} \)[/tex]:
[tex]\[
0.2666666666666667 \times 10^{-9}
\][/tex]
5. Express the result in proper scientific notation:
[tex]\( 0.2666666666666667 \)[/tex] can be written as [tex]\( 2.666666666666667 \times 10^{-1} \)[/tex]. Combining this with the power of [tex]\(10^{-9}\)[/tex], we get:
[tex]\[
2.666666666666667 \times 10^{-1} \times 10^{-9} = 2.666666666666667 \times 10^{-10}
\][/tex]
Therefore, the result is:
[tex]\[ 2.666666666666667 \times 10^{-10} \][/tex]
