Lesson 14
Decimal Representations of Rational Numbers
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.
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Do both of these strategies work?
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Which strategy do you prefer? Explain your reasoning.
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Write \(\frac{17}{20}\) as a decimal. Explain or show your reasoning.
Solution
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Problem 2
Write each fraction as a decimal.
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\(\sqrt{\frac{9}{100}}\)
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\(\frac{99}{100}\)
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\(\sqrt{\frac{9}{16}}\)
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\(\frac{23}{10}\)
Solution
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Problem 3
Write each decimal as a fraction.
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\(\sqrt{0.81}\)
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0.0276
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\(\sqrt{0.04}\)
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10.01
Solution
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Problem 4
Find the positive solution to each equation. If the solution is irrational, write the solution using square root or cube root notation.
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\(x^2=90\)
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\(p^3=90\)
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\(z^2=1\)
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\(y^3=1\)
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\(w^2=36\)
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\(h^3=64\)
Solution
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(From Unit 8, Lesson 13.)Problem 5
Here is a right square pyramid.
![A right square pyramid.](https://cms-im.s3.amazonaws.com/i7TZEWPobmWLGWebNFtTmTw9?response-content-disposition=inline%3B%20filename%3D%228-8.8.B.PP.Image.28.png%22%3B%20filename%2A%3DUTF-8%27%278-8.8.B.PP.Image.28.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171313Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b7593719878226b9234268a8edb9a09ee934c0aa0cb297acf5a7bb3f3e9c1a03)
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What is the measurement of the slant height \(\ell\) of the triangular face of the pyramid? If you get stuck, use a cross section of the pyramid.
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What is the surface area of the pyramid?
Solution
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(From Unit 8, Lesson 10.)