Tom divided numbers expressed in scientific notation as follows: $$\begin{aligned} A&=(1.76\times10^5)∶ (3.2\times10^7)\cr A&=0.55 \times 10^2\cr A&=5.5 \times 10^1 \end{aligned}$$
His classmates commented on his solution. Who is right?
Matej: The whole solution is correct.
Pavol: The solution is not correct. The correct result, expressed correctly in scientific notation, is $A=0.55 \times 10^2=5.5 \times 10^3$.
Sven: The solution is not correct. The mistake was made in dividing the powers of $10$. The correct solution is as follows. $$A=0.55 \times 10^{-2}=5.5 \times 10^{-3}$$
Jozef: The correct result, expressed correctly in scientific notation, is $A=0.55 \times 10^2$.
Sven
Matej
Pavol
Jozef
When dividing the powers of ten, we must use the rule: $a^s:a^r=a^{s-r}$. $$\begin{aligned} A&=(1.76\times10^5)∶ (3.2\times10^7)\cr A&=0.55 \times10^{-2} \end{aligned}$$ A number is expressed correctly in scientific notation when a number between $1$ and $10$ is multiplied by a power of $10$. $$A=5.5 \times 10^{-3}$$