Sure, let's solve the division problem step-by-step.
We need to find the value of [tex]\( \frac{81.09}{0.09} \)[/tex].
To make the division simpler, we can eliminate the decimal points by multiplying both the numerator and the denominator by 100:
[tex]\[ \frac{81.09 \times 100}{0.09 \times 100} = \frac{8109}{9} \][/tex]
Now, let's divide 8109 by 9.
1. Divide 81 by 9:
[tex]\[ 81 \div 9 = 9 \][/tex]
This gives us the first two digits of the quotient, which is 9.
2. Divide 09 by 9:
[tex]\[ 09 \div 9 = 1 \][/tex]
This gives us the last digit of the quotient, which is 1.
Putting these results together gives us:
[tex]\[ \frac{8109}{9} = 901 \][/tex]
Thus,
[tex]\[ \frac{81.09}{0.09} = 901 \][/tex]
So, the correct answer is [tex]\( \boxed{901} \)[/tex].
