Question

Translate to an equation and solve. 2.142 is what percent of \(35.7 ?\)

Short answer

Answer: 6%

Step-by-step solution

Understand the concept of percentage

To find the percentage, we use the formula: Percentage = (part / whole) * 100 Here, we are given the part (2.142) and the whole (35.7) and we need to find the percentage that represents the given part.

Formulate the equation

Using the percentage formula, we create the following equation: Percentage = (2.142 / 35.7) * 100

Calculate the result

Now we substitute the given values in the equation: Percentage = (2.142 / 35.7) * 100 Percentage = 0.06 * 100

Solve for the percentage

Finally, we solve the equation to find the percentage: Percentage = 6 So, 2.142 is 6% of $35.7.

Key concepts

Percent Formula

The percent formula is essential when you want to expressone number as a percentage of another. This formula allowsus to find out how much of a whole is represented by a part.Understanding this builds a strong foundation for solving variouspercentage problems. The formula can be explained as follows:

• Percentage = \( \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \)

This formula helps in transforming a ratio or fractioninto a percentage, which is a number expressed in hundredths.Furthermore, the magic of this formula is its simplicity. Oncevalues for the "part" and "whole" are identified, the formulareadily translates them into a percentage.
For example, if you want to find out what percentage 2.142is of 35.7, you simply assign these numbers to the formula.Here, \(2.142\) is the "part," and \(35.7\) is the "whole."Substituting these into the formula, you calculate the percentage as\( \left( \frac{2.142}{35.7} \right) \times 100 \). Thisprovides a clear conversion into the percentage you seek.

Percentage Equation

A percentage equation is an equation formulated tofind the percentage of a number relative to another.It uses the core concept of ratios and proportions butexpressed in percentage form. To set up a percentage equation:

• Identify the part and the whole in the problem.
• Use the percent formula by placing these into theircorrect positions in the equation.

The equation in our problem scenario becomes:\[\text{Percentage} = \left( \frac{2.142}{35.7} \right) \times 100\]This equation transfers the relationship between thenumber \(2.142\) and \(35.7\) into a percentage representation.This methodology ensures that the calculations are straightforward.Breaking down the fraction \( \frac{2.142}{35.7} \) first introducesa decimal value, which is then converted into a percentage bymultiplying by 100.This straightforward conversion helps understanding percent problemseasier because it follows a consistent process every time.

Percent Conversion

Percentage conversion is the final step where wetransform the decimal fraction into a percentage.After setting up the percentage equation, you performthe division \(2.142 \div 35.7\) which results in a decimal.This decimal is a way of expressing the part relativeto the whole before converting it to the more convenientform of percentage. This decimal is 0.06.
Once you have your decimal, percent conversion iseasily done by multiplying the decimal by 100.This conversion changes the decimal to a percentage,which in this exercise is \(0.06 \times 100 = 6\%\).

• This conversion is necessary because percentages areeasier to understand and compare. They are part ofof daily communication in contexts like discounts, probability,and statistical data.
• Mastering this conversion allows you to quickly expressparts of any whole quantitatively, making numerical insightsmore accessible across many fields.