Question

Which statement is correct?

Answer 1

Answer:

$(2.06*10^{-2})( 1.88*10^{-1}) < \frac{7.69*10^{-2}}{2.3*10^{-5}}$

Step-by-step explanation:

Verify each statement

Part 1) we have

$(2.06*10^{-2})( 1.88*10^{-1}) < \frac{7.69*10^{-2}}{2.3*10^{-5}}$

Solve the left side

$(2.06*10^{-2})( 1.88*10^{-1})=(2.06*1.88)*10^{-2-1}$

$(3.8728)*10^{-3}$

Solve the right side

$\frac{7.69*10^{-2}}{2.3*10^{-5}}=\frac{7.69}{2.3}*10^{-2+5}$

$3.3435*10^{3}$

substitute in the inequality

$(3.8728)*10^{-3} < 3.3435*10^{3}$

$0.0038728 < 3,343.5$  -----> is true

therefore

The statement is correct

Part 2) we have

$(2.06*10^{-2})( 1.88*10^{-1}) \geq \frac{7.69*10^{-2}}{2.3*10^{-5}}$

Solve the left side

$(2.06*10^{-2})( 1.88*10^{-1})=(2.06*1.88)*10^{-2-1}$

$(3.8728)*10^{-3}$

Solve the right side

$\frac{7.69*10^{-2}}{2.3*10^{-5}}=\frac{7.69}{2.3}*10^{-2+5}$

$3.3435*10^{3}$

substitute in the inequality

$(3.8728)*10^{-3} \geq 3.3435*10^{3}$

$0.0038728 \geq 3,343.5$ -----> is not true

therefore

The statement is not correct

Part 3) we have

$(2.06*10^{-2})( 1.88*10^{-1}) > \frac{7.69*10^{-2}}{2.3*10^{-5}}$

Solve the left side

$(2.06*10^{-2})( 1.88*10^{-1})=(2.06*1.88)*10^{-2-1}$

$(3.8728)*10^{-3}$

Solve the right side

$\frac{7.69*10^{-2}}{2.3*10^{-5}}=\frac{7.69}{2.3}*10^{-2+5}$

$3.3435*10^{3}$

substitute in the inequality

$(3.8728)*10^{-3} > 3.3435*10^{3}$

$0.0038728 > 3,343.5$ -----> is not true

therefore

The statement is not correct

Part 4) we have

$(2.06*10^{-2})( 1.88*10^{-1}) = \frac{7.69*10^{-2}}{2.3*10^{-5}}$

Solve the left side

$(2.06*10^{-2})( 1.88*10^{-1})=(2.06*1.88)*10^{-2-1}$

$(3.8728)*10^{-3}$

Solve the right side

$\frac{7.69*10^{-2}}{2.3*10^{-5}}=\frac{7.69}{2.3}*10^{-2+5}$

$3.3435*10^{3}$

substitute in the equation

$(3.8728)*10^{-3} = 3.3435*10^{3}$

$0.0038728 = 3,343.5$ -----> is not true

therefore

The statement is not correct