Question

Which statement is correct?

Answer 1

`(2.06*10^(-2))( 1.88*10^(-1)) < (7.69*10^(-2))/(2.3*10^(-5))`

Explanation:

Verify each statement

Part 1) we have

`(2.06*10^(-2))( 1.88*10^(-1)) < (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

`(7.69*10^(-2))/(2.3*10^(-5))=(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 (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

`(7.69*10^(-2))/(2.3*10^(-5))=(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)) > (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

`(7.69*10^(-2))/(2.3*10^(-5))=(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)) = (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

`(7.69*10^(-2))/(2.3*10^(-5))=(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