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Answer :
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].
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].
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