Let's solve the given problem step by step.
### Part a) Compare the given fractions with [tex]\( \frac{1}{9} \)[/tex]
We need to determine which of the given fractions are greater than [tex]\( \frac{1}{9} \)[/tex]. Here are the fractions we need to compare:
[tex]\[
\frac{1}{8}, \quad \frac{1}{3}, \quad \frac{1}{10}, \quad \frac{5}{9}, \quad \frac{1}{90}
\][/tex]
#### Step-by-Step Comparison:
1. Compare [tex]\( \frac{1}{8} \)[/tex] with [tex]\( \frac{1}{9} \)[/tex]
- [tex]\( \frac{1}{8} = 0.125 \)[/tex]
- [tex]\( \frac{1}{9} \approx 0.111 \)[/tex]
- Since [tex]\( 0.125 > 0.111 \)[/tex], [tex]\( \frac{1}{8} \)[/tex] is greater than [tex]\( \frac{1}{9} \)[/tex].
2. Compare [tex]\( \frac{1}{3} \)[/tex] with [tex]\( \frac{1}{9} \)[/tex]
- [tex]\( \frac{1}{3} \approx 0.333 \)[/tex]
- [tex]\( \frac{1}{9} \approx 0.111 \)[/tex]
- Since [tex]\( 0.333 > 0.111 \)[/tex], [tex]\( \frac{1}{3} \)[/tex] is greater than [tex]\( \frac{1}{9} \)[/tex].
3. Compare [tex]\( \frac{1}{10} \)[/tex] with [tex]\( \frac{1}{9} \)[/tex]
- [tex]\( \frac{1}{10} = 0.1 \)[/tex]
- [tex]\( \frac{1}{9} \approx 0.111 \)[/tex]
- Since [tex]\( 0.1 < 0.111 \)[/tex], [tex]\( \frac{1}{10} \)[/tex] is not greater than [tex]\( \frac{1}{9} \)[/tex].
4. Compare [tex]\( \frac{5}{9} \)[/tex] with [tex]\( \frac{1}{9} \)[/tex]
- [tex]\( \frac{5}{9} \approx 0.556 \)[/tex]
- [tex]\( \frac{1}{9} \approx 0.111 \)[/tex]
- Since [tex]\( 0.556 > 0.111 \)[/tex], [tex]\( \frac{5}{9} \)[/tex] is greater than [tex]\( \frac{1}{9} \)[/tex].
5. Compare [tex]\( \frac{1}{90} \)[/tex] with [tex]\( \frac{1}{9} \)[/tex]
- [tex]\( \frac{1}{90} \approx 0.011 \)[/tex]
- [tex]\( \frac{1}{9} \approx 0.111 \)[/tex]
- Since [tex]\( 0.011 < 0.111 \)[/tex], [tex]\( \frac{1}{90} \)[/tex] is not greater than [tex]\( \frac{1}{9} \)[/tex].
#### Conclusion for Part a:
The fractions greater than [tex]\( \frac{1}{9} \)[/tex] are:
[tex]\[
\frac{1}{8}, \quad \frac{1}{3}, \quad \frac{5}{9}
\][/tex]
Thus, the correct selections are [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( D \)[/tex].
### Part b) Converting [tex]\( \frac{1}{9} \)[/tex] to a Percentage
To convert [tex]\( \frac{1}{9} \)[/tex] to a percentage:
1. [tex]\( \frac{1}{9} \approx 0.1111 \)[/tex]
2. To find the percentage, multiply by 100:
[tex]\[
0.1111 \times 100 \approx 11.1111 \%
\][/tex]
3. Rounding to the nearest whole number:
[tex]\[
11.1111 \% \approx 11 \%
\][/tex]
#### Conclusion for Part b:
The nearest percentage for [tex]\( \frac{1}{9} \)[/tex] is [tex]\( 11 \% \)[/tex]. Hence, the correct answer is [tex]\( 11 \% \)[/tex].
