Arrange the following mathematical values in order from least to greatest.

The correct order from least to greatest is

4 \times 10^{-2}

2^{-3}

\sqrt{0.09}

, and

\frac{3^2}{2 \times 10^1}

By converting each value to a decimal, we find

4 \times 10^{-2} = 0.04

2^{-3} = 0.125

\sqrt{0.09} = 0.3

, and

\frac{3^2}{2 \times 10^1} = 0.45

. Ordering these decimals from smallest to largest yields the correct sequence.

Convert the scientific notation expression

4 \times 10^{-2}

to its decimal form.

4 \times 10^{-2} = 0.04

Multiplying by

10^{-2}

is equivalent to moving the decimal point of the coefficient

4

two places to the left.

Convert the negative exponent expression

2^{-3}

to a fraction and then to a decimal.

2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125

A negative exponent indicates the reciprocal of the base raised to the positive power.

Evaluate the square root of the decimal

\sqrt{0.09}

\sqrt{0.09} = 0.3

The square root of a decimal less than

1

results in a larger decimal value because

0.3 \times 0.3 = 0.09

Evaluate the exponential fraction expression

\frac{3^2}{2 \times 10^1}

\frac{3^2}{2 \times 10^1} = \frac{9}{20} = 0.45

Simplify the numerator to

9

and the denominator to

20

, then divide to find the decimal equivalent.

Compare the evaluated decimal values to determine the correct order from least to greatest.

0.04 < 0.125 < 0.3 < 0.45

, which correspond to

4 \times 10^{-2} < 2^{-3} < \sqrt{0.09} < \frac{3^2}{2 \times 10^1}

Comparing decimal place values shows that

0.04

is the smallest and

0.45

is the largest.

Converting and comparing exponential, radical, and scientific notation expressions to a common decimal format.

Question