Problem 4 - Technical Mathematics with Calculus

Question

Convert each decimal to a percent. $$0.563$$

Step-by-Step Solution

Answer

0.563 as a percent is 56.3%.

Step 1: Understanding Decimal to Percent Conversion

To convert a decimal to a percent, you multiply the decimal by 100 and add the percent sign (%). This is because 'percent' means 'per hundred'.

Step 2: Multiply the Decimal by 100

Multiply 0.563 by 100. To do this, you can shift the decimal point two places to the right, which gives you 56.3.

Step 3: Add the Percent Sign

After multiplying by 100, the last step is to add the percent sign to the number to denote that it's a percentage. Therefore, 56.3 becomes 56.3%.

Key Concepts

Percentages

Percentages are a way to express numbers as parts of a whole, specifically parts of 100. This concept is used in various aspects of daily life such as calculating discounts, interest rates, and even in measuring performance.

For instance, if we say 25%, it means 25 out of 100, or 25 parts of a whole that is divided into 100 equal parts. The symbol for percent is %, which effectively translates to 'per hundred' in Latin. Understanding percentages is crucial since they allow for a standardized way of comparing different quantities.

Decimal Numbers

Decimal numbers are a way to express fractions and parts of a whole using base ten. They consist of a whole number part, a decimal point, and a fractional part. For instance, the decimal number 0.563 has a whole number part of 0 and a fractional part of 563.

Familiarity with decimal numbers is essential for a variety of mathematical applications, from basic arithmetic to more complex equations. Decimals allow for precise representation of values and are particularly useful when dealing with non-integer quantities in measurements or financial calculations.

Mathematical Conversion

Mathematical conversion is a process that changes numbers from one form or unit to another without altering the value. It's fundamental in diverse fields such as science, finance, and everyday life. For example, converting miles to kilometers or decimal numbers to percentages are common types of conversions.

Learning the principles of conversion is essential because it allows for seamless transition between different units of measurement, enabling comparison, evaluation, and application of data in various contexts.

Basic Arithmetic

Basic arithmetic involves operations such as addition, subtraction, multiplication, and division—the fundamental building blocks for more advanced mathematical concepts. When it comes to converting decimals to percentages, multiplication plays a key role.

In the context of the given exercise, multiplying the decimal number by 100 is a simple arithmetic operation that shifts the decimal point two places to the right. Understanding this basic arithmetic operation is vital for anyone wanting to become proficient in more complex mathematics as well as for everyday scenarios like figuring out taxes or interest rates.