Given x = 3.6 \times 10^{-3} and y = 1.2 \times 10^{-4}, which of the following statements… — GRE General Test

Given $x = 3.6 \times 10^{-3}$ and $y = 1.2 \times 10^{-4}$ , which of the following statements are true? Select all that apply.

The statement that

x

is greater than

y

and the statement that the ratio

\frac{x}{y}

is equal to

30

are both correct.

The statement asserting that

x

is greater than

y

is true because

3.6 \times 10^{-3} = 0.0036

is larger than

1.2 \times 10^{-4} = 0.00012

. The statement regarding the ratio

\frac{x}{y}

is true because dividing coefficients

\frac{3.6}{1.2} = 3

and subtracting exponents

-3 - (-4) = 1

yields

3 \times 10^1 = 30

Convert both numbers to standard decimal notation to compare them.

x = 0.0036

and

y = 0.00012

Converting to standard form makes place value comparison direct.

Compare

x

and

y

0.0036 > 0.00012

, so

x > y

The thousandths digit of

x

(

3

) is greater than the thousandths digit of

y

(

0

Calculate the ratio

\frac{x}{y}

using properties of exponents.

\frac{3.6 \times 10^{-3}}{1.2 \times 10^{-4}} = \left(\frac{3.6}{1.2}\right) \times 10^{-3 - (-4)} = 3 \times 10^1 = 30

Divide the coefficients and subtract the exponents for scientific notation division.

Decimals and Scientific Notation Operations

Soru