Question

What does 8.4 10^5-7.7 10^4 equal?

Answer 1

`\huge\boxed{763,000=7.63\cdot10^5}`

Explanation:

`\bold{METHOD\ 1:}\\\\8.4\cdot10^5-7.7\cdot10^4=8.4\cdot100,000-7.7\cdot10,000\\\\=840,000-77,000=763,000\\\\\bold{METHOD\ 2:}\\\\8.4\cdot10^5-7.7\cdot10^4=8.4\cdot10^(1+4)-7.7\cdot10^4\qquad\text{use}\ a^n\cdot a^m=a^(n+m)\\\\=8.4\cdot10^1\cdot10^4-7.7\cdot10^4=84\cdot10^4-7.7\cdot10^4\\\\\text{use the distributive property}:\qquad a(b+c)=ab+ac\\\\=(84-7.7)\cdot10^4=76.3\cdot10^4=7\underbrace{.63}_(\leftarrow1)\cdot10^(4+1)=7.63\cdot10^5`