# Lesson 14

Decimal Representations of Rational Numbers

### Problem 1

Andre and Jada are discussing how to write $$\frac{17}{20}$$ as a decimal.

Andre says he can use long division to divide $$17$$ by $$20$$ to get the decimal.

Jada says she can write an equivalent fraction with a denominator of $$100$$ by multiplying by $$\frac{5}{5}$$, then writing the number of hundredths as a decimal.

1. Do both of these strategies work?

2. Which strategy do you prefer? Explain your reasoning.

3. Write $$\frac{17}{20}$$ as a decimal. Explain or show your reasoning.

### Problem 2

Write each fraction as a decimal.

1. $$\sqrt{\frac{9}{100}}$$

2. $$\frac{99}{100}$$

3. $$\sqrt{\frac{9}{16}}$$

4. $$\frac{23}{10}$$

### Problem 3

Write each decimal as a fraction.

1. $$\sqrt{0.81}$$

2. 0.0276

3. $$\sqrt{0.04}$$

4. 10.01

### Problem 4

Find the positive solution to each equation. If the solution is irrational, write the solution using square root or cube root notation.

1. $$x^2=90$$

2. $$p^3=90$$

3. $$z^2=1$$

4. $$y^3=1$$

5. $$w^2=36$$

6. $$h^3=64$$

### Solution

(From Unit 8, Lesson 13.)

### Problem 5

Here is a right square pyramid.

1. What is the measurement of the slant height $$\ell$$ of the triangular face of the pyramid? If you get stuck, use a cross section of the pyramid.

2. What is the surface area of the pyramid?