Final answer:
By dividing the total fabric (1.08 × 10^6 yards) by the fabric required per dress (5 yards) and adjusting the result into proper scientific notation, we find that 2.16 × 10^5 dresses can be produced by the factory in one year.
Step-by-step explanation:
The question is asking how many dresses can be manufactured if each requires 5 yards of fabric and the factory has 1.08 × 106 yards of fabric available for dress production for the year. To solve this, we will use the concept of division in scientific notation.
To calculate the number of dresses that can be made, we divide the total fabric available by the fabric required per dress. In this case, we divide 1.08 × 106 yards of fabric by 5 yards of fabric per dress. Here's the calculation:
1.08 × 106 yards / 5 yards = (1.08 / 5) × 106
Performing the division of the numbers gives us:
0.216 × 106
This is not in proper scientific notation, as scientific notation requires that there be only one number to the left of the decimal point. To convert it into proper scientific notation, we shift the decimal one place to the right and decrease the exponent by one:
2.16 × 105
This result means the textile factory can produce 2.16 × 105 dresses in a year with their entire production of fabric.