Problem 38 - Algebra 1

Question

Round to the nearest tenth. A total of 382 kilograms of lunar samples (rocks, dust, and so on) were collected during the six Apollo moon landings between 1969 and 1972. About \(7.5 \%\) of the lunar samples (by weight) have been analyzed and then returned for storage in the Return Sample Vault at NASA's Johnson Space Center. What is the combined weight of the samples in this vault?

Step-by-Step Solution

Answer

After the calculations, we find that the combined weight of the samples in the vault is approximately 28.7 kilograms (rounded to the nearest tenth).

Step 1: Identify the Total Weight of the Lunar Samples

The total weight of the lunar samples collected is given as 382 kilograms.

Step 2: Calculate the Weight of the Analyzed Samples

To find the weight of the analyzed samples, we multiply the total weight by 0.075 (which is the decimal equivalent of 7.5%). So, the calculation would be \(382 \times 0.075\).

Step 3: Round to the Nearest Tenth

The result from step 2 will likely be a number with many digits after the decimal point. Since we're asked to round to the nearest tenth, we look at the hundredths place. If it's 5 or greater, we round the tenths place up by one. If it's less than 5, we leave the tenths place as it is.

Key Concepts

Lunar Samples Weight Calculation

Understanding the 'lunar samples weight calculation' begins with grasping the concept of total weight and percentages. The Apollo moon landings collected a significant amount of material, totaling 382 kilograms. To determine the weight of lunar samples in the Return Sample Vault, a small fraction of the total collection, specifically 7.5%, needs to be calculated. This percentage represents what has been analyzed and preserved.

To perform this calculation:

• Start with the total weight of the lunar samples: 382 kilograms.
• Multiply this weight by the percentage (as a decimal), which is the portion of samples in the vault.

This specific operation yields the weight of the lunar samples stored following analysis and is an essential step in logging and understanding the scientific endeavours associated with space exploration.

Decimal Multiplication

When multiplying decimals, such as during 'decimal multiplication', it is crucial to align the numbers vertically and apply the same rules as with whole numbers. Remember, however, that the total number of digits after the decimal in the factors determines the number of digits after the decimal in the product.

As in our lunar sample calculation,

• Locate the decimal point in the percentage (7.5% becomes 0.075).
• Multiply it by the total weight (382 kg).
• Follow the multiplication rules as for whole numbers.

Finally, place the decimal in the answer, ensuring it reflects the correct place value determined by the original numbers. This process underpins many scientific and mathematical computations, where precision is paramount.

Percentage to Decimal Conversion

Many students struggle with the concept of 'percentage to decimal conversion', but it's a simple process once you understand the basic rule: to convert a percentage to a decimal, divide by 100. This is done by simply moving the decimal point two places to the left.

For example, with our percentage of lunar samples:

• Take 7.5%.
• Move the decimal two places to the left, yielding 0.075.

This step is fundamental in various calculations, especially when dealing with proportions and ratios in scientific data, financial figures, or statistical results. By mastering this skill, students can handle a wide range of problems effortlessly.