Convert [tex]$1 \frac{38}{45}$[/tex] into a decimal.

[tex]$1 \frac{38}{45} = $[/tex] [tex]\square[/tex]

Use "bar(number)" to indicate a repeating decimal. Examples:

[tex]0 . \overline{5} = 0 . \operatorname{bar}(5)[/tex]

[tex]0 . \overline{23} = 0 . \operatorname{bar}(23)[/tex]

[tex]0.8 \overline{3} = 0.8 \operatorname{bar}(3)[/tex]

To convert the mixed number [tex]$1 \frac{38}{45}$[/tex] into a decimal, follow these steps:

1. Understand the Mixed Number: A mixed number like [tex]$1 \frac{38}{45}$[/tex] consists of a whole number and a fraction. Here, the whole number is 1, and the fraction is [tex]$\frac{38}{45}$[/tex].

2. Convert the Fraction to Decimal: We need to convert the fraction [tex]$\frac{38}{45}$[/tex] into a decimal by dividing the numerator by the denominator.

[tex]\[
\frac{38}{45} \approx 0.8444444444444444
\][/tex]

This result is a repeating decimal. The repeating part can be represented using a bar.

3. Combine with the Whole Number: Add the decimal from the fraction to the whole number part of the mixed number.

[tex]\[
1 + 0.8444444444444444 \approx 1.8444444444444446
\][/tex]

This can be written as:

[tex]\[
1.8\operatorname{bar}(4)
\][/tex]

The [tex]$\operatorname{bar}(4)$[/tex] indicates that the digit '4' repeats indefinitely.

Therefore, the decimal representation of [tex]$1 \frac{38}{45}$[/tex] is approximately [tex]$1.8\operatorname{bar}(4)$[/tex].