Question

Estimate how many times larger 7 x 10^10 is than 13 x 10^8.

A) 50 times larger
B) 100 times larger
C) 200 times larger
D) 400 times larger

Answer 1

The answer to this equation is A) 50 times larger

Answer 2

Answer:- A) is the right answer.
`7*10^(10)` is 50 times larger than
`13*10^(8)`

Explanation:-

To estimate the number of times
`7*10^(10)` is larger than
`13*10^(8)`

Let
`7*10^(10)` is larger than
`13*10^(8)` by n times.

then
`7*10^(10)`
`=n*13*10^(8)`

`\Rightarrow\ n=(7*10^(10))/(13*10^(8))\\\\\Rightarrow\ n=(7*10^(10-8))/(13).......[by\ law\ of\ exponents\ (a^m)/(a^n)=a^(m-n)]\\\\\Rightarrow\ n=(7*10^2)/(13)\\\\\Rightarrow\ n=(7*100)/(13)\\\\\Rightarrow\ n=(700)/(13)=53.84\approx50`

[as 53.84 is near to 50 by rounding off it to the nearest ten it becomes 50]

Thus
`7*10^(10)` is 50 times larger than
`13*10^(8)`