A chemistry lab technician measures the concentration of sugar by weight in four distinct … — ACT

A chemistry lab technician measures the concentration of sugar by weight in four distinct liquid samples:

• Sample P: $\frac{7}{16}$
• Sample Q: $0.425$
• Sample R: $44\%$
• Sample S: $\frac{4}{9}$

Which of the following lists the four samples in order from least sugar concentration to greatest sugar concentration?

The correct order from least to greatest concentration is Sample Q, Sample P, Sample R, and Sample S.

To arrange the values from least to greatest, convert all numbers to decimals: Sample Q is

0.425

; Sample P is

\frac{7}{16} = 0.4375

; Sample R is

44\% = 0.44

; and Sample S is

\frac{4}{9} = 0.4444\dots

. Comparing these decimals gives

0.4250 < 0.4375 < 0.4400 < 0.4444\dots

, which corresponds to the sequence Sample Q, Sample P, Sample R, Sample S.

Convert each fraction, decimal, and percentage to a common decimal representation.

Sample P = 7/16 = 0.4375; Sample Q = 0.425; Sample R = 44% = 0.44; Sample S = 4/9 ≈ 0.4444...

Converting all numbers to decimals allows for direct place-value comparison.

Compare the converted decimal values from left to right.

0.4250 < 0.4375 < 0.4400 < 0.4444...

Comparing digits at the hundredths and thousandths places establishes the relative sizes.

Map the ordered decimal values back to their original sample names.

Sample Q < Sample P < Sample R < Sample S

Ordering matches the decimal values calculated: 0.425 < 0.4375 < 0.44 < 0.4444...

Converting mixed numerical forms (fractions, decimals, percentages) to a single decimal format for ordering.

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