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Chapter 1: Problem 111

The mass of substance is \(75.5 \mathrm{gm}\) and its volume is $25 \mathrm{~cm}^{3}$. It's density up to the correct significant figure is \(\ldots \ldots \ldots \ldots \ldots\) (a) \(3.02 \mathrm{gm} / \mathrm{cm}^{3}\) (b) \(3.200 \mathrm{gm} / \mathrm{cm}^{3}\) (c) \(3.02 \mathrm{gm} / \mathrm{cm}^{3}\) (d) \(3.1 \mathrm{gm} / \mathrm{cm}^{3}\)

Short Answer

Expert verified
The correct answer is options (a) and (c): \( 3.02 \ \mathrm{gm/cm^{3}} \).

Step by step solution

01

Identify the given values

The mass of the substance is given as \(75.5 \ \mathrm{gm}\), and the volume is \(25 \ \mathrm{cm^{3}}\).
02

Calculate the density

To calculate the density, we will use the formula Density = Mass / Volume given by: Density = \( \frac{75.5 \ \mathrm{gm}}{25 \ \mathrm{cm^{3}}} \)
03

Simplify the expression

We can simplify the expression by dividing 75.5 by 25: Density = \( \frac{75.5}{25} \ \mathrm{gm/cm^{3}} \) = \( 3.02 \ \mathrm{gm/cm^{3}} \)
04

Write the answer in the correct significant figure format

The answer obtained is already in the correct significant figure format (two decimal places), as both the mass (75.5 gm) and volume (25 cm³) have two significant figures. So the answer is: Density = \( 3.02 \ \mathrm{gm/cm^{3}} \) Comparing the calculated density with the options provided: (a) \(3.02 \ \mathrm{gm/cm^{3}}\) - Correct (b) \(3.200 \ \mathrm{gm/cm^{3}}\) - Incorrect; too many significant figures (c) \(3.02 \ \mathrm{gm/cm^{3}}\) - Repeated option, still correct (d) \(3.1 \ \mathrm{gm/cm^{3}}\) - Incorrect; incorrect significant figure The correct answer is options (a) and (c): \( 3.02 \ \mathrm{gm/cm^{3}} \).

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