Arrange the following four mathematical expressions in order from least to greatest value:

The correct order from least to greatest is

S

P

R

, and

Q

, which correspond to the decimal values

0.16 < 0.25 < 0.28 < 0.3

Evaluating each term yields decimal values:

S = 0.16

P = 0.25

R = 0.28

, and

Q = 0.3

. Ordering these from least to greatest gives

0.16 < 0.25 < 0.28 < 0.3

, which corresponds to the sequence

S, P, R, Q

Convert the fractional squared expression

S

to a decimal.

S = \left(\frac{2}{5}\right)^2 = \frac{4}{25} = 0.16

Squaring a fraction involves squaring both the numerator and denominator, then converting the resulting fraction to decimal form.

Convert the negative exponent expression

P

to a decimal.

P = 4^{-1} = \frac{1}{4} = 0.25

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

Convert the scientific notation expression

R

to a decimal.

R = 2.8 \times 10^{-1} = 0.28

Multiplying by

10^{-1}

shifts the decimal point one position to the left.

Convert the square root expression

Q

to a decimal.

Q = \sqrt{0.09} = 0.3

Finding the square root of a decimal less than

1

results in a value larger than the original decimal, since

0.3 \times 0.3 = 0.09

Compare the resulting decimal values to order them from least to greatest.

0.16 < 0.25 < 0.28 < 0.3

, so the order is

S < P < R < Q

Ordering the converted decimal values yields the correct final arrangement.

Converting exponential, radical, and scientific notation expressions to decimals to compare and order their values.

Question