Mathematics: Answer all questions for points pleas 1. solve and show your work for each question. (a) what is 0.36 ( 36 repeating ) expressed as a fraction in simplest form? (b) what is 0.36 ( 6 repeating ) expressed as a fraction in simplest form? (c) what is 0.36 expressed as a fraction in simplest form? 2. jaclyn estimates the square root of 50 in the following way: (a) explain why her reasoning is incorrect. (b) estimate the square root of 50 to the nearest tenth without using your calculator. show your

Uh, divide that number by ten?...

Answer all questions for points pleas 1. solve

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xelynncaldera

22.07.2019

1a. a standard trick: take $x=0.363636\ldots$ . then $100x=36.363636\ldots$ , which means $100x-x=99x=36$ , and so $x=\dfrac{36}{99}=\dfrac4{11}$ .1b. if $x=0.3666\ldots$ , then $10x=3.666\ldots$ and $100x=36.666\ldots$ . from this we get $100x-10x=90x=33$ , so $x=\dfrac{33}{90}=\dfrac{11}{30}$ .1c. $0.36=\dfrac{36}{100}=\dfrac9{25}$ 2a. $\sqrt{50}=\sqrt{2\cdot25}\neq2\sqrt{25}$ . jaclyn cannot pull the factor 2 from the square root like that.2b. we know $7^2=49$ and $8^2=64$ , so it must be that $x^2=50$ for some number $x$ between 7 and 8, and probably closer to 7 than 8. try computing $7.1^2$ and work up/down from there as needed.3a. similar to (2b). you know that $1^2=1$ and $2^2=4$ , so $x^2=3$ for some $1< x< 2$ . the value of $2\sqrt3$ can be estimated by doubling what you get for $\sqrt3$ . similarly, $2^2=4$ and $3^2=9$ , so $y^2=5$ for some $2< y< 3$ . you should already know that $\pi\approx3.1$ .3b. it should be quite clear that $\sqrt3< 2\sqrt3$ , and $\sqrt3< \sqrt5$ by the argument above. we know $\sqrt5< 3< 3.1< \pi$ . so the hardest part here is comparing $2\sqrt3$ and $\sqrt5$ , but this is easily done once you figure out (3a).

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