To solve the given expression [tex]\(\frac{\sqrt{169}}{225} \div \frac{121}{81}\)[/tex], we'll follow these steps:
1. Simplify the square root:
[tex]\[
\sqrt{169} = 13
\][/tex]
2. Write the simplified fraction:
[tex]\[
\frac{13}{225}
\][/tex]
3. Rewrite the division of fractions as multiplication by the reciprocal:
Division of fractions follows the rule [tex]\(\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}\)[/tex]. Therefore, we can rewrite our expression as:
[tex]\[
\frac{13}{225} \times \frac{81}{121}
\][/tex]
4. Multiply the two fractions:
When multiplying fractions, multiply the numerators together and the denominators together:
[tex]\[
\frac{13 \times 81}{225 \times 121}
\][/tex]
This results in:
[tex]\[
\frac{1053}{27225}
\][/tex]
5. Convert to decimal (if necessary):
To understand the numerical value of the fraction, we can divide the numerator by the denominator:
[tex]\[
\frac{1053}{27225} \approx 0.038677685950413224
\][/tex]
Thus, the simplified value for [tex]\(\frac{\sqrt{169}}{225} \div \frac{121}{81}\)[/tex] is approximately [tex]\(0.0387\)[/tex].
