1-1: Rational Numbers as Decimals

​1-1 Rational Numbers as Decimals

By Sallymar Tomassini Lebron

Match

Match each repeating decimal with an equivalent fraction.

• $$0.2\overline{4}$$

• $$0.1\overline{8}$$

• $$0.\overline{36}$$

• $$0.2\overline{53}$$

• $$0.\overline{28}$$

• $$\frac{22}{90}=\frac{11}{45}$$

• $$\frac{17}{90}$$

• $$\frac{36}{99}=\frac{4}{11}$$

• $$\frac{251}{990}$$

• $$\frac{28}{99}$$

Multiple Select

Select all the fractions that are equivalent to $$4.\overline{05}$$ .

• $$\frac{405}{99}$$

• $$\frac{401}{99}$$

• $$\frac{81}{33}$$

• $$\frac{802}{198}$$

• $$\frac{405}{100}$$

Multiple Choice

Choose the mixed number that is equivalent to this decimal.

3.242424…

• $$3\frac{8}{33}$$

• $$3\frac{12}{25}$$

• $$3\frac{1}{4}$$

• $$3\frac{1}{5}$$

Multiple Choice

Which fraction is equivalent to $$16.\overline{6}\ \%$$ ?

• $$\frac{1}{6}$$

• $$\frac{1}{3}$$

• $$\frac{3}{5}$$

• $$\frac{2}{3}$$

Labeling

Drag the fraction that is equivalent to each repeating decimal. Each fraction may be used only once.

Drag labels to their correct position on the image

Multiple Choice

Express the repeating decimal $$2.\overline{1}$$ as a fraction.

• $$\frac{21}{10}$$

• $$\frac{20}{9}$$

• $$\frac{19}{9}$$

• $$\frac{19}{8}$$

Math Response

A manufacturer determines that the cost of making a computer component is ​$4.191919.

Write the repeating decimal cost as a fraction.

Type answer here

Correct Answer: \frac{415}{99}

Deg^°

Rad

Dropdown

Write 0.1212.... as a fraction

x =​

Select answer

100x =​​

Select answer

100x - x = ​

Select answer

- ​

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99x = ​ ​ 12

x = ​

Select answer

Dropdown

Write 4.7272.... as a fraction

x =​

Select answer

100x =​​

Select answer

100x - x = ​

Select answer

-​

Select answer

99x = ​ ​ 468

x = ​

Select answer

Multiple Choice

Consider the decimal 0.27227222722227... and answer the following questions.

• The decimal number is rational because there is a clear pattern in the decimal digits with the number of 2s before each 7.

• The decimal number is irrational because even though the decimal digits follow a​ pattern, the decimal is not a repeating decimal.

• 
  The decimal number is irrational because there is no pattern in the digits of the decimal.

• 
  The decimal number is rational because it is composed of only 2s and 7s.

Dropdown

Brianna asked 45 students if they would vote for her to be the student council president. She used her calculator to compare the number of students who said yes with the total number of students. Her calculator showed the result as 0.6222.... Answer parts a and b.


a) Write this number as a fraction.​

​

Select answer

b) How many students said they would vote for​ Brianna?

​

Select answer

Fill in the Blanks

Consider the decimal 0.27227222722227... and answer the following question.

The next 6 digits in the decimal number are

Dropdown

Consider the decimal 0.27227222722227... and answer the following question.

From the first appearance of 7 in the ​

Select answer

​position, the next 7 is ​

Select answer

​  places to the right. The next 7 is ​

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places to the​ right, then ​places, then ​

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​places, and so on