Question

4.8 bar connotation on top of the 8. Is that number rational or irrational

Answer 1

The notation "4.8 with a bar on top of the 8" indicates that the 8 is a repeating decimal, meaning it repeats indefinitely. Thus, the number can be represented as \( 4.8888\ldots \).

Any number that can be expressed in the form of a fraction (where both the numerator and the denominator are integers) is considered a rational number. The repeating decimal \( 4.8888\ldots \) can be converted into a fraction as follows:

Let \( x = 4.8888\ldots \).

To eliminate the repeating part, multiply by 10:

\[
10x = 48.8888\ldots
\]

Now, subtract the original equation from this new equation:

\[
10x - x = 48.8888\ldots - 4.8888\ldots
\]

This simplifies to:

\[
9x = 44
\]

Now, divide both sides by 9:

\[
x = \frac{44}{9}
\]

Since \( \frac{44}{9} \) is a ratio of two integers, it confirms that \( 4.8888\ldots \) is a rational number. Thus, the number \( 4.8\overline{8} \) is rational.

Answer 2

can you show me the 4.8 with a bar notation on top of the 8

Answer 3

Certainly! The notation for \( 4.8 \) with a bar over the \( 8 \) looks like this:

\[
4.8\overline{8}
\]

The bar above the \( 8 \) indicates that the \( 8 \) repeats indefinitely, so it represents the number \( 4.88888\ldots \).

Answer 4

say that again and show me without any of these signs: /, \, |, (, ), [,],{,}

Answer 5

Sure! The notation for 4.8 with a bar over the 8, indicating that the 8 repeats indefinitely, can be expressed as:

4.8 with a line over the 8

This represents the number 4.88888 continuing on forever.