Question

Perform the indicated operations. Which of the following solutions is strongest: \(0.0125 \%, 0.25 \%, 0.1 \% ?\)

Short answer

The strongest solution is \(0.25\%\).

Step-by-step solution

Convert Percentages to Decimal Form

First, convert each percentage to a decimal. This helps in comparing the numbers more easily. - For \(0.0125\%\), move the decimal two places to the left: \[0.0125\% = \frac{0.0125}{100} = 0.000125\]- For \(0.25\%\), move the decimal two places to the left: \[0.25\% = \frac{0.25}{100} = 0.0025\]- For \(0.1\%\), move the decimal two places to the left: \[0.1\% = \frac{0.1}{100} = 0.001\]

Compare the Decimal Values

Now compare the decimal values obtained for each percentage:- \(0.000125\) from \(0.0125\%\)- \(0.0025\) from \(0.25\%\)- \(0.001\) from \(0.1\%\)Since \(0.0025\) is the largest among the decimals, \(0.25\%\) is the strongest solution.

Key concepts

Decimals

In mathematics, decimals are a way of representing fractions without necessarily using a fraction bar. A decimal uses a period as a separator between the whole number and the fractional part.
For example, the decimal 0.5 represents the fraction \(\frac{5}{10}\). In decimals, the position of each digit after the decimal point is important. It indicates tenths, hundredths, thousandths, and so on.

Understanding decimals is key because they provide a concise and straightforward way to handle divisions and precise measurements:

• For percentages, converting them to decimals makes calculations easier.
• When you see a decimal, like 0.0025, know that it means \(2.5\) thousandths, or \(\frac{25}{10000}\).

Making use of decimals helps in various math problems, ranging from basic arithmetic to complex scientific computations.

Comparing Numbers

Comparing numbers is essential to understand which of two or more values is larger or smaller. This concept becomes particularly interesting when dealing with small or large numbers in decimal form.
When comparing decimals, it is crucial to look at each place value from left to right. The first digit that differs between the numbers will indicate which one is greater or lesser.

For instance, consider these decimals: 0.000125, 0.001, and 0.0025:

• Start comparing from the leftmost digit. If the numbers are the same, continue to the next digit to the right.
• Here, 0.0025 is clearly larger than the others because it has a 2 in the thousandths place while the others have zeros there.
• If comparing decimals with different lengths, add zeros to make them the same length without changing their value.

By understanding and practicing this skill, you'll find it easier to rank percentages, fractions, or even measurements in everyday situations.

Mathematical Operations

Mathematical operations such as addition, subtraction, multiplication, and division are everyday tools used to solve problems. When dealing with percentages, for instance, mathematical operations help us convert them into decimals, which are easier to compare.
converting a percentage to a decimal requires dividing by 100, effectively a specific mathematical operation.

Here's how you can think of it:

• To convert 0.25% to a decimal, you perform the division: \(\frac{0.25}{100} = 0.0025\).
• This operation simplifies the value, aiding in computations such as comparing strengths or concentrations.

These operations form the backbone of solving many mathematical problems. Relating to real-world applications, understanding these basics lets you handle finances, measurements, and scientific data more effectively.