Question

Pleaseeeeeeeeeeee

How to write the following in scientific notation :
a. (5×〖10〗^3 )×(3.5×〖10〗^(-1)
b. (8×〖10〗^2 )÷(4×〖10〗^3 )
c. (6×〖10〗^(-3) )^2

Answer 1

`\text{The scientific notation:}\\\\a*10^n\\\\1\leq a<10,\ n\in\mathbb{Z}`

`a.\\(5*10^3)*(3.5*10^(-1))=(5*3.5)*(10^3*10^(-1))\\\\=15.75*10^(3+(-1))=15.75*10^2=1.575*10*10^2\\\\=1.575*10^(1+2)=\boxed{1.575*10^3}`

`b.\\(8*10^2)/(4*10^3)=(8/4)*(10^2/10^3)=2*10^(2-3)\\\\=\boxed{2*10^(-1)}`

`c.\\(6*10^(-3))^2=6^2*(10^(-3))^2=36*10^(-3\cdot2)=36*10^(-6)=3.6*10*10^(-6)\\\\=3.6*10^(1+(-6))=\boxed{3.6*10^(-5)}`

`Used:\\\\a^n* a^m=a^(n+m)\\\\a^n/ a^m=a^(n-m)\\\\(a^n)^m=a^(n\cdot m)`