Question

The number a x 10 ^-2 is about 8 times greater than b x 10^-3. Find the correct value of a and b.

A. a = 3.1 and b = 2.5
B. a = 2.5 and b = 3.1
C. a = 2 and b = 1.2
D. a = 1.2 and b = 2

Answer 1

Looks like is B because
.025 is about 8 times bigger then 0.0031

Answer 2

B. a = 2.5 and b = 3.1

Explanation:

In option A,

If a = 3.1, b = 2.5,

`a* 10^(-2)=3.1* 10^(-2)=0.031`

`b* 10^(-3)=2.5* 10^(-3)=0.0025`

`(a* 10^(-2))/(b* 10^(-3))=(0.031)/(0.0025)=12.4`

In option B,

If a = 2.5, b = 3.1,

`a* 10^(-2)=2.5* 10^(-2)=0.025`

`b* 10^(-3)=3.1* 10^(-3)=0.0031`

`(a* 10^(-2))/(b* 10^(-3))=(0.025)/(0.0031)=8.06451\approx 8`

In option C,

If a = 2, b = 1.2,

`a* 10^(-2)=2* 10^(-2)=0.02`

`b* 10^(-3)=1.2* 10^(-3)=0.0012`

`(a* 10^(-2))/(b* 10^(-3))=(0.02)/(0.0012)=16.6667`

In option D,

If a = 1.2, b = 2,

`a* 10^(-2)=1.2* 10^(-2)=0.012`

`b* 10^(-3)=2* 10^(-3)=0.002`

`(a* 10^(-2))/(b* 10^(-3))=(0.012)/(0.002)=6`

Hence, OPTION B is correct.