1.1 Rational and Irrational Numbers Write each fraction as a decimal or each decimal as a fraction. $$ \begin{array}{lll} ext { 1. } \frac{7}{20} & ext { 2. } 1 . \overline{27} & ext { 3. } 1 \frac{7}{8} \ ext { Solve each equation for } x . & ext { 5. } x^{3}=343 & ext { 6. } x^{2}=\frac{1}{100}\end{array} $$ $$ \begin{array}{lll} ext { 4. } x^{2}=81 & ext { (0) } & ext { ( }\end{array} $$

Question

1.1 Rational and Irrational Numbers Write each fraction as a decimal or each decimal as a fraction. $$ \begin{array}{lll}	ext { 1. } \frac{7}{20} & 	ext { 2. } 1 . \overline{27} & 	ext { 3. } 1 \frac{7}{8} \ 	ext { Solve each equation for } x . & 	ext { 5. } x^{3}=343 & 	ext { 6. } x^{2}=\frac{1}{100}\end{array} $$ $$ \begin{array}{lll}	ext { 4. } x^{2}=81 & 	ext { (0) } & 	ext { ( }\end{array} $$

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Sure, let's solve each of the problems step by step.

## 1. Writing $$ \frac{7}{20} $$ as a Decimal

To convert the fraction $$ \frac{7}{20} $$ to a decimal, divide the numerator by the denominator:

$$
\frac{7}{20} = 7 \div 20 = 0.35
$$

**Answer:** $$ 0.35 $$

---

## 2. Writing $$ 1.\overline{27} $$ as a Fraction

The notation $$ 1.\overline{27} $$ represents a repeating decimal where "27" repeats indefinitely. To convert this to a fraction, follow these steps:

Let $$ x = 1.\overline{27} $$.

Multiply both sides by 100 (since "27" has two digits):

$$
100x = 127.\overline{27}
$$

Subtract the original equation from this new equation:

$$
100x - x = 127.\overline{27} - 1.\overline{27}
$$
$$
99x = 126
$$
$$
x = \frac{126}{99}
$$

Simplify the fraction by dividing numerator and denominator by 9:

$$
x = \frac{14}{11}
$$

**Answer:** $$ \frac{14}{11} $$

---

## 3. Writing $$ 1 \frac{7}{8} $$ as a Decimal

First, convert the mixed number to an improper fraction:

$$
1 \frac{7}{8} = \frac{8 \times 1 + 7}{8} = \frac{15}{8}
$$

Now, divide the numerator by the denominator to get the decimal:

$$
\frac{15}{8} = 15 \div 8 = 1.875
$$

**Answer:** $$ 1.875 $$

---

## 4. Solving $$ x^{2} = 81 $$ for $$ x $$

To solve for $$ x $$, take the square root of both sides:

$$
x^{2} = 81
$$
$$
x = \pm \sqrt{81}
$$
$$
x = \pm 9
$$

**Answer:** $$ x = 9 $$ or $$ x = -9 $$

---

## 5. Solving $$ x^{3} = 343 $$ for $$ x $$

To solve for $$ x $$, take the cube root of both sides:

$$
x^{3} = 343
$$
$$
x = \sqrt[3]{343}
$$
$$
x = 7
$$

**Answer:** $$ x = 7 $$

---

## 6. Solving $$ x^{2} = \frac{1}{100} $$ for $$ x $$

To solve for $$ x $$, take the square root of both sides:

$$
x^{2} = \frac{1}{100}
$$
$$
x = \pm \sqrt{\frac{1}{100}}
$$
$$
x = \pm \frac{1}{10}
$$
$$
x = \pm 0.1
$$

**Answer:** $$ x = 0.1 $$ or $$ x = -0.1 $$

---

If you have any further questions or need additional explanations, feel free to ask!
1. $$ \frac{7}{20} = 0.35 $$ 2. $$ 1.\overline{27} = \frac{14}{11} $$ 3. $$ 1 \frac{7}{8} = 1.875 $$ 4. $$ x^{2} = 81 $$ → $$ x = 9 $$ or $$ x = -9 $$ 5. $$ x^{3} = 343 $$ → $$ x = 7 $$ 6. $$ x^{2} = \frac{1}{100} $$ → $$ x = 0.1 $$ or $$ x = -0.1 $$

1.1 Rational and Irrational Numbers
Write each fraction as a decimal or each decimal as a fraction.

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