Express the following decimal inches to fractional dimensions to the nearest sixteenth of an inch. 79.8 in = \frac{\text{__}}{16}
The Correct Answer and Explanation is:
To convert a decimal measurement in inches (79.8 inches) into a fraction with a denominator of 16, we will first convert the decimal to a fraction and then round it to the nearest sixteenth.
Step 1: Convert the Decimal Part to a Fraction
Start by separating the whole number from the decimal part:
- Whole number: 79
- Decimal part: 0.8
Now, express 0.8 as a fraction:0.8=8100.8 = \frac{8}{10}0.8=108
Next, simplify this fraction. Both the numerator and denominator can be divided by 2:810=45\frac{8}{10} = \frac{4}{5}108=54
Step 2: Convert the Fraction to a Denominator of 16
We now need to express 45\frac{4}{5}54 with a denominator of 16. To do this, multiply both the numerator and denominator by 16 ÷ 5 = 3.2 (we’ll round it to 3 for simplicity):45=4×35×3=1215\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}54=5×34×3=1512
Thus, 79.8 inches would be approximately expressed as a mixed fraction.
