(2) Convert each of the following to (i) a fraction in its simplest form, (ii) a decimal. (a) $$ 7 \% $$ (b) $$ 30 \% $$ (c) $$ 65 \% $$ (d) $$ 160 \% $$ Arrange the following in ascending order. $$ 1 \frac{3}{4} \%, \quad 2.2 \%, \quad \frac{1}{8} \%, \quad 0.01 \%, \quad 33.9 \%, \quad 200 \% $$ (4) Express $$ P $$ as a percentage of $$ Q $$ in each of the following (a) $$ P=\$ 250, Q=\$ 1000 $$ (b) $$ P=12 \mathrm{~m}, Q=15 \mathrm{~m} $$ (c) $$ P=20 \mathrm{~kg}, Q=25 \mathrm{~kg} $$ (d) $$ P=375 \mathrm{~cm}^{3}, Q=200 \mathrm{~cm}^{2} $$ (3) Express $$ Y $$ as a percentage of $$ X $$ in each of the following. (a) $$ X=4 \mathrm{~h}, Y=30 \mathrm{~min} $$ (b) $$ X=3 e, Y=120 \mathrm{ml} $$ (c) $$ X=6 \mathrm{~m}, Y=95 \mathrm{~cm} $$ (d) $$ X=5 \mathrm{~kg}, Y=75 \mathrm{~g} $$ (3) Find the value of each of the following. (a) $$ 40 \% $$ of 120 cm (b) $$ 15 \% $$ of $$ 360^{\circ} $$ (c) $$ 66 \frac{2}{3} \% $$ of 54 s (d) $$ 130 \% $$ of $$ \$ 200 $$ (7) Mr Singh's monthly salary is $$ \$ 4800 $$. He rents a room that costs him $$ \$ 1200 $$ per month.

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Let's break down the problem step by step.

### Part 1: Convert Percentages to Fractions and Decimals

#### (a) Convert $$ 7\% $$
1. **Fraction**: 
   $$
   \frac{7}{100}
   $$
   This is already in simplest form.
   
2. **Decimal**: 
   $$
   0.07
   $$

#### (b) Convert $$ 30\% $$
1. **Fraction**: 
   $$
   \frac{30}{100} = \frac{3}{10}
   $$
   This is in simplest form.
   
2. **Decimal**: 
   $$
   0.30
   $$

#### (c) Convert $$ 65\% $$
1. **Fraction**: 
   $$
   \frac{65}{100} = \frac{13}{20}
   $$
   This is in simplest form.
   
2. **Decimal**: 
   $$
   0.65
   $$

#### (d) Convert $$ 160\% $$
1. **Fraction**: 
   $$
   \frac{160}{100} = \frac{8}{5}
   $$
   This is in simplest form.
   
2. **Decimal**: 
   $$
   1.60
   $$

### Part 2: Arrange in Ascending Order

We need to convert the percentages to decimals for easy comparison:
- $$ 1 \frac{3}{4} \% = 1.75\% = 0.0175 $$
- $$ 2.2\% = 0.022 $$
- $$ \frac{1}{8} \% = 0.125\% = 0.00125 $$
- $$ 0.01\% = 0.0001 $$
- $$ 33.9\% = 0.339 $$
- $$ 200\% = 2.0 $$

Now, arranging these in ascending order:
1. $$ 0.0001 \% $$ (0.01%)
2. $$ 0.00125 \% $$ (1/8%)
3. $$ 0.0175 \% $$ (1 3/4%)
4. $$ 0.022 \% $$ (2.2%)
5. $$ 0.339 \% $$ (33.9%)
6. $$ 2.0 \% $$ (200%)

### Part 3: Express $$ P $$ as a Percentage of $$ Q $$

The formula to express $$ P $$ as a percentage of $$ Q $$ is:
$$
\text{Percentage} = \left( \frac{P}{Q} \right) \times 100
$$

#### (a) $$ P=\$ 250, Q=\$ 1000 $$
$$
\text{Percentage} = \left( \frac{250}{1000} \right) \times 100 = 25\%
$$

#### (b) $$ P=12 \mathrm{~m}, Q=15 \mathrm{~m} $$
$$
\text{Percentage} = \left( \frac{12}{15} \right) \times 100 = 80\%
$$

#### (c) $$ P=20 \mathrm{~kg}, Q=25 \mathrm{~kg} $$
$$
\text{Percentage} = \left( \frac{20}{25} \right) \times 100 = 80\%
$$

#### (d) $$ P=375 \mathrm{~cm}^{3}, Q=200 \mathrm{~cm}^{2} $$
$$
\text{Percentage} = \left( \frac{375}{200} \right) \times 100 = 187.5\%
$$

### Part 4: Express $$ Y $$ as a Percentage of $$ X $$

Using the same formula:
$$
\text{Percentage} = \left( \frac{Y}{X} \right) \times 100
$$

#### (a) $$ X=4 \mathrm{~h}, Y=30 \mathrm{~min} $$
Convert $$ 30 \mathrm{~min} $$ to hours:
$$
30 \mathrm{~min} = 0.5 \mathrm{~h}
$$
$$
\text{Percentage} = \left( \frac{0.5}{4} \right) \times 100 = 12.5\%
$$

#### (b) $$ X=3e, Y=120 \mathrm{ml} $$
Assuming $$ e $$ is a constant (approximately 2.718):
$$
\text{Percentage} = \left( \frac{120}{3e} \right) \times 100 \approx \left( \frac{120}{8.154} \right) \times 100 \approx 14.7\%
$$

#### (c) $$ X=6 \mathrm{~m}, Y=95 \mathrm{~cm} $$
Convert $$ 95 \mathrm{~cm} $$ to meters:
$$
95 \mathrm{~cm} = 0.95 \mathrm{~m}
$$
$$
\text{Percentage} = \left( \frac{0.95}{6} \right) \times 100 \approx 15.83\%
$$

#### (d) $$ X=5 \mathrm{~kg}, Y=75 \mathrm{~g} $$
Convert $$ 75 \mathrm{~g} $$ to kilograms:
$$
75 \mathrm{~g} = 0.075 \mathrm{~kg}
$$
$$
\text{Percentage} = \left( \frac{0.075}{5} \right) \times 100 = 1.5\%
$$

### Part 5: Find the Value of Each Percentage

#### (a) $$ 40\% $$ of 120 cm
$$
\text{Value} = \left( \frac{40}{100} \right) \times 120 = 48 \mathrm{~cm}
$$

#### (b) $$ 15\% $$ of $$ 360^{\circ} $$
$$
\text{Value} = \left( \frac{15}{100} \right) \times 360 = 54^{\circ}
$$

#### (c) $$ 66 \frac{2}{3} \% $$ of 54 s
Convert $$ 66 \frac{2}{3} \% $$ to a fraction:
$$
66 \frac{2}{3} \% = \frac{200}{3} \%
$$
$$
\text{Value} = \left( \frac{200}{300} \right) \times 54 = 36 \mathrm{s}
$$

#### (d) $$ 130\% $$ of $$ \$ 200
(a) 40% of 120 cm is 48 cm. (b) 15% of 360° is 54°. (c) 66 2/3% of 54 s is 36 s. (d) 130% of \$200 is \$260. ### Part 6: Mr. Singh's Salary and Rent Mr. Singh's monthly salary is \$4800, and he pays \$1200 for rent each month. To find the percentage of his salary spent on rent: $$ \text{Percentage} = \left( \frac{1200}{4800} \right) \times 100 = 25\% $$ So, Mr. Singh spends 25% of his salary on rent. ### Summary of Simplified Answers: 1. **Conversions and Arrangements**: - $$ 7\% = \frac{7}{100} = 0.07 $$ - $$ 30\% = \frac{3}{10} = 0.30 $$ - $$ 65\% = \frac{13}{20} = 0.65 $$ - $$ 160\% = \frac{8}{5} = 1.60 $$ - Arranged in ascending order: 0.0001%, 0.00125%, 0.0175%, 0.022%, 0.339%, 2.0% 2. **Expressing $$ P $$ as a Percentage of $$ Q $$**: - (a) 25% - (b) 80% - (c) 80% - (d) 187.5% 3. **Expressing $$ Y $$ as a Percentage of $$ X $$**: - (a) 12.5% - (b) Approximately 14.7% - (c) Approximately 15.83% - (d) 1.5% 4. **Finding Values of Percentages**: - (a) 48 cm - (b) 54° - (c) 36 s - (d) \$260 5. **Mr. Singh's Salary and Rent**: - 25% of his salary is spent on rent.

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