Barbora multiplied numbers expressed in scientific notation. $$\begin{aligned} A&=(6.25\times10^3)\cdot(3.4\times10^4)\cr A&=21.25\times10^7\cr A&=2.125 \times 10^6 \end{aligned}$$
Her classmates commented on her solution. Who is right?
Silvia: The whole solution is correct.
Mary: The solution is not correct. The correct result, expressed correctly in scientific notation, is $A=\boldsymbol{2.125 \times 10^8}$.
Daniela: The solution is not correct. The mistake was made in multiplying the powers of ten. The correct solution is as follows: $$A=21.25 \times 10^{12}=\boldsymbol{2.125 \times10^{13}}$$
Zuzana: The correct scientific notation of the result is $A=\boldsymbol{21.25 \times 10^7}$.
Mary
Silvia
Daniela
Zuzana
When multiplying the powers of ten, we must use the rule: $a^s\cdot a^r=a^{s+r}$.
$$\begin{aligned} A&=(6.25\times10^3) \cdot (3.4\times10^4)\cr A&=21.25 \times 10^7 \end{aligned}$$
A number is expressed correctly in scientific notation when a number between $1$ and $10$ is multiplied by a power of $10$.
$$A=2.125 \times 10^8$$