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An aerospace engineering facility is calibrating a pressure sensor using four specialized metallic foils. To prevent calibration errors, a technician must stack these foils in strictly ascending order of their thickness (from thinnest to thickest).

The thicknesses of the four foils are:
- Foil P: $0.345$ mm
- Foil Q: $\frac{11}{32}$ mm
- Foil R: $0.\overline{34}$ mm
- Foil S: $\frac{7}{20}$ mm

Arrange the foils in the correct ascending order of their thickness.

Drag items to arrange them in the correct order

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Answer

The correct ascending sequence from thinnest to thickest is Foil R, Foil Q, Foil P, and Foil S.

By converting all foil thicknesses into uniform decimal representations, we establish the values: Foil R (

0.3434...

), Foil Q (

0.34375

), Foil P (

0.345

), and Foil S (

0.35

). Comparing these exact decimal values digit-by-digit confirms that the ascending sequence must be R, Q, P, then S.

Step-by-Step Solution

Convert the fraction for Foil S to a decimal.

\frac{7}{20} = \frac{7 \times 5}{20 \times 5} = \frac{35}{100} = 0.35

Converting all measurements to a uniform decimal format allows for direct magnitude comparison.

Convert the fraction for Foil Q to a decimal.

11 \div 32 = 0.34375

Using long division provides the exact decimal expansion necessary to compare against closely grouped measurements.

Expand the recurring decimal for Foil R.

0.\overline{34} = 0.343434...

Expanding the repeating digits to at least 4 decimal places makes place-value comparison clear.

Compare all four decimal values place-by-place and sequence them from smallest to largest.

0.343434... < 0.34375 < 0.34500 < 0.35000

Aligning the decimals by their thousandths and ten-thousandths places reveals the exact ascending sequence.

Key Concept

Converting fractions and recurring decimals into standard decimals to accurately evaluate and compare their magnitudes.

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