Convert 0.8 to a rational number

Question

Convert  0.8 to a rational number
0.8 is a repeating decimal

GPT-4o mini · Answer

The decimal 0.8 can be expressed as a rational number. It is not a repeating decimal; it is a terminating decimal.

To convert 0.8 to a rational number:

Recognize that 0.8 can be written as $\frac{8}{10}$.
Simplify $\frac{8}{10}$ by dividing the numerator and denominator by their greatest common divisor, which is 2.

\[ \frac{8 \div 2}{10 \div 2} = \frac{4}{5} \]

Therefore, the rational form of 0.8 is $\frac{4}{5}$.

..... · Answer

0.8 repeats

GPT-4o mini · Answer

If the decimal is $0.888...$, which is a repeating decimal, we can convert it to a rational number as follows: Let $x = 0.888...$. 1. Multiply both sides by 10 to shift the decimal point: $$ 10x = 8.888... $$ 2. Now, you have two equations: $$ x = 0.888... $$ $$ 10x = 8.888... $$ 3. Subtract the first equation from the second: $$ 10x - x = 8.888... - 0.888... $$ $$ 9x = 8 $$ 4. Solve for $x$: $$ x = \frac{8}{9} $$ Thus, if $0.8$ is meant as a repeating decimal ($0.888...$), its rational form is $\frac{8}{9}$. If you meant $0.8$ as a non-repeating number, the rational form is $\frac{4}{5}$. Please clarify if you meant $0.888...$.

..... · Answer

yes i did mean 0.888...

GPT-4o mini · Answer

Great! Since you meant $0.888...$ (which represents the repeating decimal), we already found that: $$ x = 0.888... $$ 1. Multiply both sides by 10: $$ 10x = 8.888... $$ 2. Subtract the first equation from the second: $$ 10x - x = 8.888... - 0.888... $$ $$ 9x = 8 $$ 3. Solve for $x$: $$ x = \frac{8}{9} $$ Therefore, the rational representation of $0.888...$ is $\frac{8}{9}$.