standard_description: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
problem_activity: Problem 1
Write each rational number in the form
$${a\over{b}}$$
, where
$$a$$
and
$$b$$
are integers, and
$$b\neq0$$
.
a.
$${0.3333}$$
b.
$${-5.05}$$
c.
$${\sqrt{64}}$$
e.
$${\sqrt{4\over25}}$$
f.
$${\sqrt{1.21}}$$
Problem 2
A student wrote two repeating decimals as fractions using the strategy shown below.
| Given the decimal                       $$0.\overline{12}$$                       Let                       $$x=0.\overline{12}$$                       Then                         $$100x=12.\overline{12}$$              |https://d37su8u1z9ynie.cloudfront.net/uploads/2019/02/06/math8_u7_l5_ap2a.PNG|  |https://d37su8u1z9ynie.cloudfront.net/uploads/2019/02/06/math8_u7_l5_ap2a.PNG| image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2019/02/06/math8_u7_l5_ap2a.PNG | Given the decimal                       $$0.\overline{123}$$                       Let                       $$x=0.\overline{123}$$                       Then                       $$1000x=123.\overline{123}$$             |https://d37su8u1z9ynie.cloudfront.net/uploads/2019/02/06/math8_u7_l5_ap2b.PNG|  |https://d37su8u1z9ynie.cloudfront.net/uploads/2019/02/06/math8_u7_l5_ap2b.PNG| image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2019/02/06/math8_u7_l5_ap2b.PNG |
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a.   Describe the student’s strategy in your own words.
b.   Use the same strategy to write the two decimals below as fractions.
$${0.\overline{54}}$$
$${0.1\overline{23}}$$
Problem 3
What is the sum of
$${0.1}$$
and
$${0.\overline3}$$
written as a fraction?


aligns: yes