Final answer:
The numbers a) 0.7866666666..., b) -73.00025252525...., c) 40.864301019654885385....., and d) -9.707121221222122221.... can be expressed in scientific notation as 7.8666666666 x 10^-1, -7.3000252525 x 10^1, 4.0864301019654885385 x 10^1, and -9.707121221222122221... x 10^0 respectively.
Step-by-step explanation:
a) 0.7866666666...:
This number represents a repeating decimal, as the digits after the decimal point repeat indefinitely. We can express this number in scientific notation as 7.8666666666... x 10-1.
b) -73.00025252525....:
This number has a repeating decimal part as well. In scientific notation, it can be written as -7.3000252525... x 101.
c) 40.864301019654885385.....:
This number does not have any repeating decimals. It can be expressed in scientific notation as 4.0864301019654885385... x 101.
d) -9.707121221222122221....:
Similarly to the previous examples, this number has a repeating decimal part. In scientific notation, it can be written as -9.707121221222122221... x 100.