Sure! Let's solve the division step by step.
Given the expression:
[tex]\[ \frac{10 \times 10^{-6}}{5 \times 10^{-5}} \][/tex]
First, let's write out the numerator and the denominator in a more recognizable form. We have:
Numerator: [tex]\( 10 \times 10^{-6} \)[/tex]
Denominator: [tex]\( 5 \times 10^{-5} \)[/tex]
Next, let's simplify both the numerator and the denominator:
Numerator: [tex]\(10 \times 10^{-6} = 10^{-5} \)[/tex]
Denominator: [tex]\(5 \times 10^{-5} = 5 \times 10^{-5} \)[/tex]
Now we perform the division:
[tex]\[ \frac{10 \times 10^{-6}}{5 \times 10^{-5}} = \frac{10^{-5}}{5 \times 10^{-5}} \][/tex]
This is equivalent to:
[tex]\[ \frac{10 \times 10^{-6}}{5 \times 10^{-5}} = \frac{10}{5} \times \frac{10^{-6}}{10^{-5}} \][/tex]
Simplify the fractions separately:
[tex]\[ \frac{10}{5} = 2 \][/tex]
And:
[tex]\[ \frac{10^{-6}}{10^{-5}} = 10^{-1} \][/tex]
Combining these results, we have:
[tex]\[ 2 \times 10^{-1} = 0.2 \][/tex]
Hence, the final result is:
[tex]\[ 0.2 \][/tex]
So,
[tex]\[ \frac{10 \times 10^{-6}}{5 \times 10^{-5}} = 0.2 \][/tex]
