Question

Explain fundamental theorem of arithmetic and decimal expansion of rational numbers

Answer 1

According to the Fundamental Theorem of Arithmetic, every integer greater than 1 is either prime or a product of primes and that product is unique.
The prime factorization of $8=2\times 2\times 2$
No other number can have the same prime factorization.
Decimal expansion can be understood by taking an example.
eg- 0.1234 can be written as $\left(\frac{1}{10}\right)+\left(\frac{2}{100}\right)+\left(\frac{3}{1000}\right)+\left(\frac{4}{10000}\right)$