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

Option B.

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* 3\cdot 10^6=6\cdot 10^8`

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

`x=(6\cdot 10^8)/(3\cdot 10^6)`

`x=2\cdot (10^8)/(10^6)`

Using the property of exponent, we get

`x=2\cdot 10^(8-6)`
`(\because (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.

Answer 2

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

Explanation:

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

To compare both values we divide the exponents

`(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)

`(10^8)/(10^6)=10^2`

`(6*10^8)/(3*10^6)=2*10^2= 200`

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