Convert to a fraction in simplest form: 2.388888 dots 2(7)/(18) 2(38)/(99) 2(3)/(8) 2(38)/(100) 2(38)/(90)

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Convert to a fraction in simplest form:  2.388888 dots  2(7)/(18)  2(38)/(99)  2(3)/(8)  2(38)/(100)  2(38)/(90)

Bytelearn · Accepted Answer

Identify repeating part: First, let's identify the repeating part of the decimal. The repeating part is ＂88＂, so we can write the decimal as 2.3 with 88 repeating. To convert this into a fraction, we'll let x equal the repeating decimal: x = 2.388888...Multiply by 100: Next, we multiply x by 100, since the repeating part is two digits long, to shift the decimal two places to the right: 100x = 238.888888...Subtract original: Now, we subtract the original x from 100x to get rid of the repeating part: 100x - x = 238.888888... - 2.388888... 99x = 236.5Solve for x: We then solve for x by dividing both sides of the equation by 99: x = 236.5 / 99Separate whole number: Now, we simplify the fraction. First, we separate the whole number from the decimal: x = 2 + 36.5 / 99Rewrite fraction: We notice that 36.5 can be written as 365/10, so we rewrite the fraction: x = 2 + (365/10) / 99Simplify numerator and denominator: To simplify further, we multiply the numerator and denominator by 10 to get rid of the decimal in the numerator: x = 2 + (365 * 10) / (99 * 10) x = 2 + 3650 / 990Further simplify fraction: We can now simplify the fraction 3650/990 by dividing both the numerator and the denominator by their greatest common divisor, which is 10: x = 2 + 365 / 99Correct simplification: The fraction 365/99 can be further simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 73: x = 2 + 5 / (99 / 73) x = 2 + 5 / (99 / 73) x = 2 + 5 / 1.355The correct simplification of 365/99 by dividing both the numerator and the denominator by their greatest common divisor, which is 73, is: x = 2 + 365 / 99 x = 2 + (365 / 73) / (99 / 73) x = 2 + 5 / 1.355 x = 2 + 5 / (135 / 73) x = 2 + 5 / (135 / 73) x = 2 + 5 / (135 / 73) x = 2 + 5 / 1.355

Convert to a fraction in simplest form: $\newline$ $2.388888 \ldots$ $\newline$ $2 \frac{7}{18}$ $\newline$ $2 \frac{38}{99}$ $\newline$ $2 \frac{3}{8}$ $\newline$ $2 \frac{38}{100}$ $\newline$ $2 \frac{38}{90}$

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Convert to a fraction in simplest form:\newline2.388888… 2.388888 \ldots 2.388888…\newline2718 2 \frac{7}{18} 2187​\newline23899 2 \frac{38}{99} 29938​\newline238 2 \frac{3}{8} 283​\newline238100 2 \frac{38}{100} 210038​\newline23890 2 \frac{38}{90} 29038​

Convert to a fraction in simplest form: $\newline$ $2.388888 \ldots$ $\newline$ $2 \frac{7}{18}$ $\newline$ $2 \frac{38}{99}$ $\newline$ $2 \frac{3}{8}$ $\newline$ $2 \frac{38}{100}$ $\newline$ $2 \frac{38}{90}$