Question

Find the total mass of two brass cylinders, which weigh \(126.457 \mathrm{~g}\) and \(131.6 \mathrm{~g}\)

Short answer

The total mass of the two brass cylinders is \(258.057 \mathrm{~g}\).

Step-by-step solution

Understand the Problem

We need to find the total mass of two brass cylinders. The individual masses given are \(126.457 \mathrm{~g}\) and \(131.6 \mathrm{~g}\). Our task is to add these two masses to find the total mass.

Align Decimal Points

Before adding, align the numbers by their decimal points. This ensures that the decimal places are correctly added together.\[\begin{array}{r}126.457 \131.600 \\hline\end{array}\]

Add the Numbers

Add the numbers starting from the rightmost digit (the thousandths place) to the left:- Thousandths place: \(7 + 0 = 7\)- Hundredths place: \(5 + 0 = 5\)- Tenths place: \(4 + 6 = 10\) (write \(0\), carry \(1\))- Units place: \((6 + 1) + 1 = 8\)- Tens place: \(2 + 3 = 5\)- Hundreds place: \(1 + 1 = 2\)Bringing everything together, we have the total mass:\[\begin{array}{r}126.457 \+131.600 \\hline258.057\end{array}\]

Conclusion

After adding the masses, the total mass of the two brass cylinders is \(258.057 \mathrm{~g}\).

Key concepts

Mass Calculation

Mass calculation involves finding the total mass of objects by adding up the individual masses. Think about each object having a weight measured in grams (g) or other units. In this exercise, we have two brass cylinders. Each of them has its mass given by their weight measurements.

• The first cylinder weighs 126.457 grams.
• The second cylinder weighs 131.6 grams.

To find the total mass of both cylinders, we simply add these two weights together. This involves understanding their placement in terms of units, tens, hundreds, etc. Once you add them up correctly, you get the total weight which gives the complete mass of both cylinders combined.

Decimal Addition

When adding numbers with decimal points, it’s crucial to align these points. This alignment ensures that digits in the same positions are added together. Let's break it down: First, align decimal numbers vertically so that the decimal points line up. This helps in correctly adding each digit from the rightmost to the left:

• Start with the thousandths, which are the smallest. Add digits in this position first.
• Move to hundredths, then tenths, units, tens, and finally hundreds.

Every time you have a sum greater than 9 in any place value, carry the extra value to the next place value on the left. This step is critical in accurate decimal addition. For example, when adding the tenths, 6 in one number and 4 in the other give 10, where 0 is left in this position, and 1 is carried over to the next place value.

Measurement Precision

Measurement precision is about how detailed a measurement is. More decimal places mean more precision. In chemistry, precision helps in providing accurate results critical for experiments and calculations. In this exercise, note how the first cylinder's mass is given to three decimal places (126.457 g), while the second is to one decimal place (131.6 g). When these are added, the answer takes up to the most specific decimal used in either number.

• This means, in this case, the total mass uses three decimal places, resulting in 258.057 g.
• Despite the first number (126.457) being more precise, the consistency of precision in results needs to respect the least precise measurement.

This approach maintains improvement accuracy and avoids giving an impression of unwarranted precision beyond what's provided in the initial data.