ack":"That digit repeats forever.","points":1},{"id":"b3b1a47c-7846-47d7-97cc-7f711d00e2fe","cardType":"basic","front":"In the decimal $0.\\dot{4}0\\dot{5}$, which digits form the repeating block?","back":"405","points":1},{"id":"c89bcb37-3f3a-47c0-aba2-8632fe2f6867","cardType":"cloze","front":"A recurring decimal is a decimal where a [ ] repeats forever.","back":"A recurring decimal is a decimal where a digit or block of digits repeats forever.","points":null},{"id":"95be9c48-fdc4-48d2-8bd5-beca1e88bc1a","cardType":"basic","front":"How is a fraction like $\\frac{5}{11}$ converted into a decimal without a calculator?","back":"Divide the numerator (5) by the denominator (11) using long division.","points":2},{"id":"f017f546-9ccc-4eca-9ff0-e98375795251","cardType":"basic","front":"When converting a fraction to a decimal using division, how do you identify that the decimal is recurring?","back":"A remainder repeats/reappears during the division process.","points":1},{"id":"ac6c7fea-ce9b-43fc-917c-516dcb350310","cardType":"basic","front":"What is the primary goal of multiplying a recurring decimal $x$ by powers of 10 in an algebraic proof?","back":"To make the infinite recurring tails match so they cancel out when subtracted.","points":2},{"id":"15e69a2c-f5d9-423f-b094-274ca9079e73","cardType":"cloze","front":"In the proof for $0.\\dot{7}$, if $x = 0.777\\ldots$, then $10x = \\text{[...]}$.","back":"In the proof for $0.\\dot{7}$, if $x = 0.777\\ldots$, then $10x = \\boxed{7.777\\ldots}$.","points":null},{"id":"1f147185-fa57-4e8f-97ca-966b621cac8a","cardType":"basic","front":"What is $0.\\dot{7}$ expressed as a fraction?","back":"$$\\frac{7}{9}$","points":1},{"id":"aacc41de-82ea-4d1d-8860-07e7ba219574","cardType":"basic","front":"For $0.5\\dot{3}$, why is subtracting $x$ from $10x$ ineffective for canceling the decimal?","back":"The tails do not match ($5.333\\ldots$ vs $0.533\\ldots$).","points":2},{"id":"59d7d69d-cdd9-46d7-99c3-2ba075f13d0c","cardType":"basic","front":"Which two multiples of $x$ should be subtracted to convert $0.5\\dot{3}$ to a fraction?","back":"

$100x$
$10x$

","points":2},{"id":"ed6135e5-5945-46bd-9485-ecee4931b02b","cardType":"cloze","front":"If a decimal has $m$ non-recurring digits and $n$ recurring digits, you use the multiples $\\text{[...]}$ and $10^{m+n}x$.","back":"If a decimal has $m$ non-recurring digits and $n$ recurring digits, you use the multiples $\\boxed{10^m x}$ and $10^{m+n}x$.","points":null},{"id":"43f7564e-8b46-418e-a42f-863f21c8dac3","cardType":"cloze","front":"If a decimal has $m$ non-recurring digits and $n$ recurring digits, you use the multiples $10^m x$ and $\\text{[...]}$.","back":"If a decimal has $m$ non-recurring digits and $n$ recurring digits, you use the multiples $10^m x$ and $\\boxed{10^{m+n}x}$.","points":null},{"id":"287ef03f-f5d2-4914-8662-1219bf483156","cardType":"basic","front":"Why is $1000x$ used when converting $0.\\dot{1}8\\dot{9}$ to a fraction?","back":"The repeating block contains 3 digits.","points":1},{"id":"28d9ed0b-469a-4d58-873f-3da6a8772924","cardType":"basic","front":"Convert $0.\\dot{1}8\\dot{9}$ to its simplest fraction form.","back":"$$\\frac{7}{37}$","points":2},{"id":"91b75dd6-035d-4c14-b02b-245e1338af11","cardType":"cloze","front":"A fraction is in its simplest form when the numerator and denominator have no [ ] greater than 1.","back":"A fraction is in its simplest form when the numerator and denominator have no common factors greater than 1.","points":null},{"id":"873047ec-4238-4b41-8df2-1b6132e2d658","cardType":"basic","front":"For $2.4\\dot{3}\\dot{6}$, which two multiples of $x$ are needed to align the recurring tails?","back":"

Recurring Decimals to Fractions Flashcards

Recurring Decimals to Fractions Flashcards

Recurring Decimals to Fractions Flashcards

Recurring Decimals to Fractions Flashcards