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. The largest rock collected weighs 11.7 kilograms. This single rock is what percent of the total weight of the samples?

Short answer

The largest rock collected comprises 3.1% of the total weight of the samples.

Step-by-step solution

Identifying the Part and the Whole

The WEIGHT of the LARGEST ROCK represents the PART for the proportion equation, which is given as 11.7 kilograms. The TOTAL WEIGHT collected during the moon missions represents the WHOLE, which is given as 382 kilograms.

Calculating the Percentage

Plug these values into the proportion equation with the weight of the rock as the part and the total weight as the whole. The equation becomes: \((11.7 / 382) * 100\)

Carrying out the Calculation

Dividing 11.7 by 382 gives approximately 0.0306. Multiply this by 100 to convert it to a percentage: \(0.0306 * 100\)

Rounding to the Nearest Tenth

The result is approximately 3.06%, but the problem asks for the answer rounded to the nearest tenth. Thus, the final result is 3.1%.

Key concepts

Proportion Equations

Proportion equations are a foundational concept in algebra that relate two ratios or fractions to one another. These equations are commonly used to solve problems that involve finding out what part of a whole something represents, much like in the exercise regarding the lunar rocks. Exactly, when we were looking to find out what percent a single rock's weight represents of the total weight,

The general form of a proportion equation looks like this: \( \frac{a}{b} = \frac{c}{d} \), where \( a \) and \( c \) are compared parts, and \( b \) and \( d \) are wholes that correspond to these parts. These equations can be solved by finding the cross-product and equating them since if two ratios are equal, the product of their extremes (outer terms) is equal to the product of their means (inner terms).

When dealing with percentages, we use the proportion equation \( \frac{part}{whole} = \frac{percent}{100} \). By isolating the 'percent' variable and solving the equation, we discover the percentage that the part represents of the whole.

Rounding Numbers

Rounding numbers is a mathematical technique used to reduce the digits in a number while keeping its value close to what it was. It's like smoothing out the numbers to make them simpler to work with or to fit a particular level of precision. When you round a number, you essentially look at the digits to the right of the desired decimal place to determine whether to increase the digit in the desired place or leave it as is.

For example, to round to the nearest tenth, which is the first place after the decimal, we look at the second digit after the decimal. If this second digit is 5 or more, we round up the first digit. Otherwise, we leave it. In the lunar rock exercise, the result of the proportion equation was 3.06%, and since the digit after the tenths place (6) is more than 5, it was rounded up to 3.1%.

Expressing Parts of a Whole

When we talk about expressing parts of a whole, we typically refer to fractions or percentages that represent a segment of a larger quantity. The 'whole' is the entirety of whatever we're examining, while the 'part' is a piece or portion of that whole. In the lunar sample problem, we looked at how a specific rock's weight compared to the total weight of all samples collected.

Expressing this relationship as a fraction, we would write it \( \frac{11.7}{382} \). To express it as a percentage, which is often more intuitive for people to understand, we convert the fraction to a percentage by multiplying by 100. This gives us a clearer picture of the relationship between the part and the whole in a different format that's often used in everyday contexts, such as sales, data analysis, and academic assessments.