Lesson 14

Decimal Representations of Rational Numbers

Let’s learn more about how rational numbers can be represented. 

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. \(h^3=64\)

(From Unit 8, Lesson 13.)

Problem 5

Here is a right square pyramid.

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?

(From Unit 8, Lesson 10.)