Volume Mass Density Dime 0.34cm3 6.6706 g/cm3 Penny 0.4332cm3 5.77 g/cm3 Quarter 0.81 cm3 7 g/cm3 Uncertainties COIN Uncertainty in mass δm (grams) (taken as EXACT) Uncertainty in Diameter δd (mm) (taken as EXACT) Uncertainty in Thickness δt (mm) (taken as EXACT) SIG FIGS dime 0.001 0.01 0.01 penny 0.001 0.01 0.01 quarter 0.001 0.01 0.01 RELATIVE UNCERTAINTIES COIN Relative Uncertainty in mass δm/m (%) Relative Uncertainty in Diameter δd/d (%) Relative Uncertainty in Thickness δt/t (%) SIG. FIGS. Dime 0.229 0.074 0.056 Penny 0.044 0.066 0.052 Quarter 0.0176 0.57 0.041 COIN Relative Uncertainty in Volume δV/V = 2*δd/d + δt/t (%) Relative Uncertainty in Mass Density δρ/ρ = δV/V + δm/m (%) SIG. FIGS. Dime 0.186 0.415 Penny 0.17 0.21 Quarter 0.652 0.669 FOR EACH COIN, CALCULATE THE UNCERTAINTY IN THE MASS DENSITY (gm/cm^3) coins Relative Uncertainty in Mass Density δρ/ρ = δV/V + δm/m (%) Mass Density ρ= m/V (grams/cm^3) UNCERTAINTY IN THE MASS DENSITY δρ (gm/cm^3) sigfigs Dime 0.894 6.67 0.0596 Penny 0.801 5.77 0.0462 Quarter 0.67 7.00 0.0469 ---------------------------------------------------------------------------------------------------------------------- FOR EACH COIN, STATE ITS MASS DENSITY (gm/cm^3) IN THE FORM ρ ± δρ COIN MASS DENSITY ρ (grams/cm^3) ROUNDED TO CORRECT SIG FIGS UNCERTAINTY IN MASS DENSITY: δρ (gm/cm^3) SIG. FIGS. ROUNDED TO SAME NUMBER OF DECIMAL PLACES AS ρ IN 1ST COLUMN ρ (gm/cm^3) δρ (gm/cm^3) ρ ± δρ (gm/cm^3) Dime
USING DATA FROM THE US MINT |
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US MINT DATA |
US MINT DATA |
US MINT DATA |
COIN |
Measured MASS m (grams) |
Measured Diameter d (mm) |
Measured Thickness t (mm) |
SIG. FIGS. |
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Dime |
2.268 |
17.91 |
1.35 |
Penny |
2.500 |
19.05 |
1.52 |
Quarter |
5.670 |
24.26 |
1.75 |
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Volume |
Mass Density |
Dime |
0.34cm3 |
6.6706 g/cm3 |
Penny |
0.4332cm3 |
5.77 g/cm3 |
Quarter |
0.81 cm3 |
7 g/cm3 |
Uncertainties
COIN |
Uncertainty in mass δm (grams) (taken as EXACT) |
Uncertainty in Diameter δd (mm) (taken as EXACT) |
Uncertainty in Thickness δt (mm) (taken as EXACT) |
SIG FIGS |
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dime |
0.001 |
0.01 |
0.01 |
penny |
0.001 |
0.01 |
0.01 |
quarter |
0.001 |
0.01 |
0.01 |
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RELATIVE UNCERTAINTIES |
COIN |
Relative Uncertainty in mass δm/m (%) |
Relative Uncertainty in Diameter δd/d (%) |
Relative Uncertainty in Thickness δt/t (%) |
SIG. FIGS. |
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|
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Dime |
0.229 |
0.074 |
0.056 |
Penny |
0.044 |
0.066 |
0.052 |
Quarter |
0.0176 |
0.57 |
0.041 |
COIN |
Relative Uncertainty in Volume δV/V = 2*δd/d + δt/t (%) |
Relative Uncertainty in Mass Density δρ/ρ = δV/V + δm/m (%) |
SIG. FIGS. |
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Dime |
0.186 |
0.415 |
Penny |
0.17 |
0.21 |
Quarter |
0.652 |
0.669 |
FOR EACH COIN, CALCULATE THE UNCERTAINTY IN THE MASS DENSITY (gm/cm^3)
coins |
Relative Uncertainty in Mass Density δρ/ρ = δV/V + δm/m (%) |
Mass Density ρ= m/V (grams/cm^3) |
UNCERTAINTY IN THE MASS DENSITY δρ (gm/cm^3) |
sigfigs |
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Dime |
0.894 |
6.67 |
0.0596 |
Penny |
0.801 |
5.77 |
0.0462 |
Quarter |
0.67 |
7.00 |
0.0469 |
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FOR EACH COIN, STATE ITS MASS DENSITY (gm/cm^3) IN THE FORM ρ ± δρ |
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COIN |
MASS DENSITY ρ (grams/cm^3) ROUNDED TO CORRECT SIG FIGS |
UNCERTAINTY IN MASS DENSITY: δρ (gm/cm^3) |
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SIG. FIGS. |
ROUNDED TO SAME NUMBER OF DECIMAL PLACES AS ρ IN 1ST COLUMN |
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ρ (gm/cm^3) |
δρ (gm/cm^3) |
ρ ± δρ (gm/cm^3) |
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Dime |
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Penny |
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Quarter |
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