Question

What is the difference in mass between a nickel that weighs \(4.8 \mathrm{~g}\) and a nickel that weighs \(4.8673 \mathrm{~g}\) ?

Short answer

The difference in mass is \(0.0673 \mathrm{~g}\).

Step-by-step solution

Identify Masses of Both Nickels

The problem provides the masses of both nickels. The first nickel has a mass of \(4.8 \mathrm{~g}\), and the second nickel has a mass of \(4.8673 \mathrm{~g}\).

Set Up the Subtraction

To find the difference in mass, set up the subtraction of the smaller mass from the larger mass: \(4.8673 \mathrm{~g} - 4.8 \mathrm{~g}\).

Perform the Subtraction

Subtract the masses. Align the decimal points and subtract: \(4.8673 - 4.8 = 0.0673 \mathrm{~g}\).

Interpret the Result

The result of the subtraction is \(0.0673 \mathrm{~g}\), which is the difference in mass between the two nickels.

Key concepts

Subtraction of Measurements

In chemistry, measurements often require subtraction, like determining the difference in mass between two objects. When subtracting measurements, it's crucial to ensure calculations are done accurately to achieve the correct result.
As seen in this exercise, we subtracted the mass of one nickel from another. We started by identifying the masses: one nickel is given as \(4.8 \mathrm{~g}\), while the other is \(4.8673 \mathrm{~g}\). To find the difference, you take the larger mass and subtract the smaller mass from it:

• Larger mass: \(4.8673 \mathrm{~g}\)
• Smaller mass: \(4.8 \mathrm{~g}\)

By subtracting these values, you determine how much more the second nickel weighs compared to the first.

Decimal Alignment

Decimal alignment is vital when handling measurements involving decimal points. Improper alignment can lead to errors in subtraction or addition. This means ensuring all decimal points are vertically aligned before performing the arithmetic operations.
In the exercise, the decimal alignment ensures the subtraction is seamless. For example, when subtracting \(4.8673\) from \(4.8\), the decimals must line up:

• Write \(4.8\) as \(4.8000\) to align with \(4.8673\).
• Subtract accordingly, focusing on one decimal place at a time.

This way, you avoid miscalculations, especially when dealing with numbers that vary in length decimal-wise.

Significant Figures in Mass Measurement

Significant figures reflect the precision of a measurement. They inform us about how reliable and detailed a measurement is, considering all numbers that carry meaning toward its precision.
In our problem, the importance of significant figures comes into play when interpreting the subtraction result. The mass \(4.8 \mathrm{~g}\) contains two significant figures, while \(4.8673 \mathrm{~g}\) has five. To express the difference in mass correctly, your answer should respect the least number of significant figures used in the measured values.

• The difference is calculated as \(0.0673 \mathrm{~g}\).
• However, given the initial values, the result should be stated respecting the lesser precision, i.e., to two significant figures: \(0.067 \mathrm{~g}\).

By applying this rule, it reflects the accurate precision of the measurements involved.