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𝙎𝙝𝙤𝙧𝙩 𝙖𝙣𝙨𝙬𝙚𝙧: 𝙄𝙛 𝙞𝙩 𝙞𝙨 𝙞𝙣 𝙩𝙝𝙚 𝙛𝙤𝙧𝙢 𝙤𝙛 𝙭𝙮 / (𝙭)(5^𝙘)(2^𝙙) 𝙞𝙩 𝙞𝙨 𝙩𝙚𝙧𝙢𝙞𝙣𝙖𝙩𝙞𝙣𝙜.

𝙀𝙭𝙥𝙡𝙖𝙣𝙖𝙩𝙞𝙤𝙣:We can say that all fractions in the form of y / 2^n (where y is any number) are terminating because 2^n x 5^n = 10^n and 10^n is terminating when divided by 100 (because it would just displace the number by 2 digits behind eg. 10^1 / 100 = 0.1), and using this same logic y / 5^n is terminating. Is that the answer? No!

1 / 50 is terminating but 50 ≠ 2 ^ n and 50 ≠ 5 ^ n.You can write this as y / (10^x / 2^n).This is equal to y / (5^n)(2^x). In fact y / 5^a = y / (5^c)(2^d) and y / (5^c)(2^d) = y / 2^b , because x^0 = 1. Is that the answer?
No!

3/150 is terminating but isn't in the form of y / (5^c)(2^d).It is terminating because it simplifies into 1/50 which is in the form of y / (5^c)(2^d).So we can write the answer as xy / (x)(5^c)(2^d).