Lesson 11
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.

Do both of these strategies work?

Which strategy do you prefer? Explain your reasoning.

Write \(\frac{17}{20}\) as a decimal. Explain or show your reasoning.
Problem 2
Write each fraction as a decimal.

\(\sqrt{\frac{9}{100}}\)

\(\frac{99}{100}\)

\(\sqrt{\frac{9}{16}}\)

\(\frac{23}{10}\)
Problem 3
Write each decimal as a fraction.

\(\sqrt{0.81}\)

0.0276

\(\sqrt{0.04}\)

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.

\(x^2=90\)

\(p^3=90\)

\(z^2=1\)

\(y^3=1\)

\(w^2=36\)

\(h^3=64\)
Problem 5
Here is a right square pyramid.

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.

What is the surface area of the pyramid?