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Difficulty: MediumFractions and Decimals

A civil engineer is evaluating the thickness of four different structural panels, measured in centimeters (cm). To meet safety standards, the panels must be stacked from the thinnest to the thickest. Arrange the following panel thicknesses in ascending order.

  1. 1Panel Z: 1381\frac{3}{8} cm
  2. 2Panel X: 107\frac{10}{7} cm
  3. 3Panel W: 1.4‾1.\overline{4} cm
  4. 4Panel Y: 1.451.45 cm

Answer

The correct ascending order from thinnest to thickest is: Panel Z, Panel X, Panel W, Panel Y.
The correct sequence is determined by converting all measurements into standard decimal forms. Panel Z is exactly 1.3751.375 cm, Panel X is approximately 1.4281.428 cm, Panel W is 1.444...1.444... cm, and Panel Y is exactly 1.4501.450 cm. Sorting these values in ascending order yields Panel Z, Panel X, Panel W, Panel Y.

Step-by-Step Solution

1
Convert the thickness of Panel Z into a standard decimal format.
Panel Z = 138=1+0.375=1.3751\frac{3}{8} = 1 + 0.375 = 1.375 cm.
Converting a mixed fraction to a decimal allows for direct magnitude comparison.
2
Convert the thickness of Panel X into a standard decimal format.
Panel X = 107≈1.42857...\frac{10}{7} \approx 1.42857... cm.
An improper fraction must be divided out to identify its exact decimal value.
3
Expand the thickness of Panel W to clearly see its decimal value.
Panel W = 1.4‾=1.4444...1.\overline{4} = 1.4444... cm.
The overline indicates a recurring decimal that continues infinitely with the digit 4.
4
Compare all four decimal values and arrange them from smallest to largest.
1.375<1.42857...<1.4444...<1.4501.375 < 1.42857... < 1.4444... < 1.450. Therefore, Panel Z < Panel X < Panel W < Panel Y.
The stem requires ordering from thinnest to thickest.

Key Concept

Converting mixed fractions, improper fractions, and recurring decimals into a common decimal format to accurately compare and order them.
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Topics

Fractions and Decimals

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