8.NS.1, 8.NS.2 Rational/Irrational Numbers

Rational/Irrational Numbers

8.NS.1, 8.NS.2

Converting decimals to fractions

• Every terminating decimal can be written as a fraction. Write the decimal number over the place value and simplify.

• Every repeating decimal can be written as a fraction using the algebraic method (see your notes).

Multiple Choice

Which of these is equivalent to 0.18181818...?

•  $\frac{2}{11}$  

•  $\frac{2}{9}$  

•  $\frac{9}{50}$  

•  $\frac{1}{18}$  

Convert a fraction to a decimal

• Divide the numerator by the denominator

Multiple Choice

Which decimal number is equivalent to

 $\frac{3}{27}$  

• 0.1

• 0.12121212...

• 9

• 0.1111...

Rational Numbers

• Can be written as fractions

• Repeating decimals (5.23232323...)

• Terminating decimals (5.23)

•  $\sqrt{25}\ =\ 5$  

  Whole numbers
  

• Mixed numbers, improper fractions ( $3\ \frac{1}{2}\ or\ \frac{7}{2}$  )

Irrational Numbers

• Cannot be written as fractions

• Nonrepeating, nonterminating decimals

•   $\pi$  
  

•  $\sqrt{5}$  

•  $6^{\frac{1}{3}}$  or the cube root of 6

Multiple Select

Select all the irrational numbers.

• $\frac{4}{7}$

• $\sqrt{30}$

• $\frac{21}{\sqrt{4}}$

• $\pi$

• $-27$

Multiple Choice

Which of these statements is correct based on the number line below?

• $\sqrt{12}$ is to the right of point B, because it is less than 4.

• $\sqrt{12}$ is between points A and B, because it is less than 0 and greater than 4.

• $\sqrt{12}$ is between points A and B, because it is greater than 0 and less than 4.

• $\sqrt{12}$ is to the right of point B, because it is greater than 4.

Multiple Choice

Brett used a calculator to find the decimal expansions of various square roots as shown. According to these expansions, which of the following expressions is the greatest?

• $3+\sqrt{15}$

• $5+\sqrt{6}$

• $8-\sqrt{3}$

• $10-\sqrt{11}$

Multiple Select

Which of these numbers is between 5 and 10 on a number line? Select all that apply.

• $\sqrt{6}$

• $-\sqrt{81}$

• $\sqrt{21}$

• $\sqrt{38}$

• $\sqrt{44}$