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

Question

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

UpStudy AI · Accepted Answer

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**

$$
0.01\%,\quad \frac{1}{8}\%,\quad 1\, \frac{3}{4}\%,\quad 2.2\%,\quad 33.9\%,\quad 200\%
$$
**Conversions and Arrangement:** 1. **7%** - **Fraction:** 7/100 - **Decimal:** 0.07 2. **30%** - **Fraction:** 3/10 - **Decimal:** 0.30 3. **65%** - **Fraction:** 13/20 - **Decimal:** 0.65 4. **160%** - **Fraction:** 8/5 - **Decimal:** 1.60 **Arranged Percentages in Ascending Order:** 0.01%, 1 1⁄4%, 2.2%, 33.9%, 200%

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