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

Answer:

B. a = 2.5 and b = 3.1

Step-by-step explanation:

In option A,

If a = 3.1, b = 2.5,

$a\times 10^{-2}=3.1\times 10^{-2}=0.031$

$b\times 10^{-3}=2.5\times 10^{-3}=0.0025$

$\frac{a\times 10^{-2}}{b\times 10^{-3}}=\frac{0.031}{0.0025}=12.4$

In option B,

If a = 2.5, b = 3.1,

$a\times 10^{-2}=2.5\times 10^{-2}=0.025$

$b\times 10^{-3}=3.1\times 10^{-3}=0.0031$

$\frac{a\times 10^{-2}}{b\times 10^{-3}}=\frac{0.025}{0.0031}=8.06451\approx 8$

In option C,

If a = 2, b = 1.2,

$a\times 10^{-2}=2\times 10^{-2}=0.02$

$b\times 10^{-3}=1.2\times 10^{-3}=0.0012$

$\frac{a\times 10^{-2}}{b\times 10^{-3}}=\frac{0.02}{0.0012}=16.6667$

In option D,

If a = 1.2, b = 2,

$a\times 10^{-2}=1.2\times 10^{-2}=0.012$

$b\times 10^{-3}=2\times 10^{-3}=0.002$

$\frac{a\times 10^{-2}}{b\times 10^{-3}}=\frac{0.012}{0.002}=6$

Hence, OPTION B is correct.