Lesson 11: Practice Problems

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 From Unit 8 Lesson 8

Here is a right square pyramid.

A right square pyramid. The side lengths of the square base are labeled 16. The slant height is labeled “L” and is indicated by a dashed line from the top vertex of the pyramid, along the middle of one of the side triangular faces. A right triangle is formed inside the pyramid by the slant height line, “L,” a dashed line from the top vertex of the pyramid, to the middle of the square, labeled 15, and by another dashed line that forms a right angle and connects along the base of the pyramid to the slant height, “L.” The slant height “L” is opposite the right angle.

What is the measurement of the slant height $ℓ$ 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?