Question

Compare 6 ⋅ 108 to 3 ⋅ 106.

6 ⋅ 108 is 2,000 times larger than 3 ⋅ 106.
6 ⋅ 108 is 200 times larger than 3 ⋅ 106.
6 ⋅ 108 is 20 times larger than 3 ⋅ 106.
6 ⋅ 108 is 2 times larger than 3 ⋅ 106.

Answer 1

Answer:

$6*10^8$  is 200 times larger than  $3*10^6$

Step-by-step explanation:

$6*10^8\ and \ 3*10^6$

To compare both values we divide the exponents

$\frac{6*10^8}{3*10^6}$

6 divide by 3 is 2

for simplify exponents we use exponential property

a^m / a^n = a^(m-n)

$\frac{10^8}{10^6}=10^2$

$\frac{6*10^8}{3*10^6}=2*10^2= 200$

$6*10^8$  is 200 times larger than  $3*10^6$

Answer 2

Answer:

Option B.

Step-by-step explanation:

The given numbers are $6\cdot 10^8$ and $3\cdot 10^6$.

Let $6\cdot 10^8$ is x times larger than $3\cdot 10^6$.

$x\times 3\cdot 10^6=6\cdot 10^8$

Divide both sides by $3\cdot 10^6$.

$x=\dfrac{6\cdot 10^8}{3\cdot 10^6}$

$x=2\cdot \dfrac{10^8}{10^6}$

Using the property of exponent, we get

$x=2\cdot 10^{8-6}$             $(\because \dfrac{a^m}{a^n}=a^{m-n})$

$x=2\cdot 10^2$

$x=2\cdot 100$

$x=200$

$6\cdot 10^8$ is 200 times larger than $3\cdot 10^6$.

Therefore, the correct option is B.