Convert each of the following to \( \begin{array}{l}\text { (i) a fraction in its simplest form, } \\ \text { (ii) a decimal. } \\ \begin{array}{ll}\text { (a) } 7 \% & \text { (b) } 30 \% \\ \text { (c) } 65 \% & \text { (d) } 160 \%\end{array} \\ \text { Arrange the following in ascending order. } \\ 1 \frac{3}{4} \%, 2.2 \%, \frac{1}{8} \%, 0,01 \%, 33.9 \% \text {, } 200 \%\end{array} \

Certainly! Let's address each part of your query systematically. ### **Part (i) and (ii): Converting Percentages** We'll convert each percentage to: 1. **A fraction in its simplest form.** 2. **A decimal.** --- #### **(a) 7 %** 1. **Fraction:** \[ 7\% = \frac{7}{100} \] This fraction is already in its simplest form. 2. **Decimal:** \[ 7\% = 0.07 \] --- #### **(b) 30 %** 1. **Fraction:** \[ 30\% = \frac{30}{100} = \frac{3}{10} \] (Simplified by dividing numerator and denominator by 10.) 2. **Decimal:** \[ 30\% = 0.30 \] --- #### **(c) 65 %** 1. **Fraction:** \[ 65\% = \frac{65}{100} = \frac{13}{20} \] (Simplified by dividing numerator and denominator by 5.) 2. **Decimal:** \[ 65\% = 0.65 \] --- #### **(d) 160 %** 1. **Fraction:** \[ 160\% = \frac{160}{100} = \frac{8}{5} \] (Simplified by dividing numerator and denominator by 20.) 2. **Decimal:** \[ 160\% = 1.60 \] --- ### **Part: Arranging Percentages in Ascending Order** Given percentages: \[ 1 \frac{3}{4}\%,\quad 2.2\%,\quad \frac{1}{8}\%,\quad 0.01\%,\quad 33.9\%,\quad 200\% \] **Step 1: Convert All to Decimal Form for Easy Comparison** 1. \( 1 \frac{3}{4}\% = 1 + \frac{3}{4}\% = 1.75\% \) 2. \( 2.2\% \) remains \( 2.2\% \) 3. \( \frac{1}{8}\% = 0.125\% \) 4. \( 0.01\% \) remains \( 0.01\% \) 5. \( 33.9\% \) remains \( 33.9\% \) 6. \( 200\% \) remains \( 200\% \) **Step 2: Arrange in Ascending Order** From smallest to largest: \[ 0.01\%,\quad \frac{1}{8}\% \ (0.125\%),\quad 1\, \frac{3}{4}\% \ (1.75\%),\quad 2.2\%,\quad 33.9\%,\quad 200\% \] --- ### **Final Arrangement** \[ 0.01\%,\quad \frac{1}{8}\%,\quad 1\, \frac{3}{4}\%,\quad 2.2\%,\quad 33.9\%,\quad 200\% \]