To solve this problem, we need to convert the given mixed fraction [tex]\( -20 \frac{3}{4} \)[/tex] into a decimal number. Here is the step-by-step solution:
1. Understand the Mixed Fraction:
The given temperature is [tex]\( -20 \frac{3}{4} \)[/tex]. This means there is a whole number part [tex]\(-20\)[/tex] and a fractional part [tex]\( \frac{3}{4} \)[/tex].
2. Convert the Fraction to a Decimal:
To convert the fractional part [tex]\( \frac{3}{4} \)[/tex] into a decimal, we perform the division:
[tex]\[ \frac{3}{4} = 0.75 \][/tex]
3. Combine the Whole Number and Decimal:
Now, combine the whole number part [tex]\(-20\)[/tex] with the decimal part [tex]\(0.75\)[/tex]:
[tex]\[ -20 + 0.75 = -20.75 \][/tex]
Thus, the chemist recorded the temperature [tex]\( -20.75 \)[/tex] in her notebook as a decimal. Therefore, the correct answer from the provided options is:
[tex]\[ \mathbf{-20.75} \][/tex]
This confirms the temperature written in the notebook.
