Question

(6x10^2)/(3x10-5) help what is this in standard form?

Answer 1

Answer:

The standard form of $\frac{6 \times 10^{2}}{3 \times 10^{-5}}$ is 20,00,0000

Solution:

Given that $\frac{6 \times 10^{2}}{3 \times 10^{-5}}$ ---- eqn 1

To write$\frac{6 \times 10^{2}}{3 \times 10^{-5}}$ in standard form,

We know that $\bold{\frac{1}{a^{-m}} = a^{m}}$ .So $\frac{1}{10^{-5}}$  becomes $10^{5}$.

Now eqn 1 becomes,

$= \frac{6 \times 10^{2}}{3} \times 10^{5}$ ----- eqn 2

We know that $\bold{a^{m} \times a^{n}=a^{m+n}}$, so $10^{2} \times 10^{5} = 10^{7}$

Now eqn 2 becomes,

$= \frac{6}{3} \times 10^{7}$

$= 2 \times 10^{7}$ ---- eqn 3

Expanding $10^{7}$:  

Here 10 is the base term and 7 is the exponent value. So base term 10 is multiplied by itself 7 times.

$10^{7} = 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10$

Now eqn 3 becomes,

$= 2 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10$

= 20,00,0000  

Hence the standard form of $\frac{6 \times 10^{2}}{3 \times 10^{-5}}$ is 20,00,0000