Question

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

Answer 1

The answer to this equation is A) 50 times larger

Answer 2

Answer:- A) is the right answer.$7\times10^{10}$ is 50 times larger than $13\times10^{8}$

Explanation:-

To estimate the number of times $7\times10^{10}$ is larger than $13\times10^{8}$

Let $7\times10^{10}$ is larger than $13\times10^{8}$  by n times.

then $7\times10^{10}$  $=n\times13\times10^{8}$

$\Rightarrow\ n=\frac{7\times10^{10}}{13\times10^{8}}\\\\\Rightarrow\ n=\frac{7\times10^{10-8}}{13}.......[by\ law\ of\ exponents\ \frac{a^m}{a^n}=a^{m-n}]\\\\\Rightarrow\ n=\frac{7\times10^2}{13}\\\\\Rightarrow\ n=\frac{7\times100}{13}\\\\\Rightarrow\ n=\frac{700}{13}=53.84\approx50$

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

Thus $7\times10^{10}$ is 50 times larger than $13\times10^{8}$