Question

Identify the strongest in each of the following. \(1: 25, \frac{1}{5}, 0.02 \%\)

Short answer

The strongest is 25.

Step-by-step solution

Convert Percent to Decimal

First, convert the percentage to a decimal form. The given percentage is 0.02%. To convert a percentage to a decimal, divide by 100. So,\[ 0.02\% = \frac{0.02}{100} = 0.0002. \]

Convert Fraction to Decimal

Next, convert the fraction to a decimal. The fraction given is \( \frac{1}{5} \). Convert it to a decimal by dividing 1 by 5:\[ \frac{1}{5} = 0.2. \]

Compare Decimal Values

Now, compare the values of the numbers in decimal form. We have 25 from the integer, 0.2 from the fraction, and 0.0002 from the percentage. The decimal forms are 25, 0.2, and 0.0002 respectively. Clearly, 25 is the largest value.

Key concepts

Fractions

Fractions are mathematical expressions representing a part of a whole. They consist of a numerator, the number above the fraction line, and a denominator, the number below the fraction line. Fractions have the form \( \frac{a}{b} \), where 'a' is the numerator and 'b' is the denominator. For instance, in the fraction \( \frac{1}{5} \), 1 is the numerator and 5 is the denominator. This means you have one out of five equal parts.Understanding fractions involves grasping the idea that the denominator tells you how many equal parts make up a whole, while the numerator tells you how many parts are being considered. If you ever need to compare fractions, it might be easier to convert them into decimals or percentages. That way, you can easily see which one represents a larger or smaller part of the whole.

Percentages

Percentages are a way to express a number as a fraction of 100. They are especially handy when you want to compare proportions. To convert any percentage to a decimal, just divide the percentage number by 100. For example, 0.02% becomes \( \frac{0.02}{100} = 0.0002 \).Think of percentages as a useful tool in real life—for instance, when calculating discounts or interest rates. When dealing with small percentages, remember that they can represent very tiny parts, as was the case with 0.02% transformed into a decimal. This can make comparisons clearer and help you solve problems that may seem tricky at first.

Decimal Conversion

Decimal conversion is a fundamental mathematical operation that involves changing a fraction or percentage into a decimal form. This process simplifies the comparison of different numbers since they can all be viewed in the same format.To convert a fraction like \( \frac{1}{5} \) to a decimal, divide the numerator by the denominator. This gives you 0.2. For percentages, conversion to decimals involves dividing the percentage value by 100, which transforms 0.02% into 0.0002. These conversions are crucial in making calculations and comparisons straightforward. When all numbers are decimals, it's easier to see which is greater or smaller at a glance.

Comparison of Numbers

Comparison of numbers is the action of determining which number is larger, smaller, or if they are equal. It is a vital skill, especially when numbers are in different forms like integers, fractions, and percentages. To simplify the comparison, converting all numbers to a uniform format—like decimals—is quite helpful.In our example, the numbers given were 25 (an integer), \( \frac{1}{5} \) (a fraction), and 0.02% (a percentage). By converting all to decimals—25.0, 0.2, and 0.0002—you can easily see 25.0 is the largest. This conversion process ensures you aren't misled by differences in number formats and can make confident comparisons in your math work.