standard_description: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
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.
{"table": [{"_attributes": {"class": ["table"], "style": "width:100%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "p": [{"_value": "Given the decimal", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$0.\\overline{12}$$"}]}, {"_value": "Let", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$x=0.\\overline{12}$$"}]}, {"_value": "Then", "u": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$100x=12.\\overline{12}$$"}]}]}, {"img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2019/02/06/math8_u7_l5_ap2a.PNG", "style": "height:113px; width:126px"}}]}]}, {"_attributes": {"style": "text-align:center"}, "p": [{"_value": "Given the decimal", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$0.\\overline{123}$$"}]}, {"_value": "Let", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$x=0.\\overline{123}$$"}]}, {"_value": "Then", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$1000x=123.\\overline{123}$$"}]}, {"img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2019/02/06/math8_u7_l5_ap2b.PNG", "style": "height:114px; width:132px"}}]}]}]}]}]}]}
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: no