Problem 20 - Prealgebra

Question

Change each percent to a decimal. $$0.6 \%$$

Step-by-Step Solution

Answer

0.6% as a decimal is 0.006.

Step 1: Understanding Percentages

A percentage is a way of expressing a number as a fraction of 100. So, 0.6% means 0.6 out of every 100, or 0.6 per 100.

Step 2: Converting Percent to Decimal

To convert a percentage to a decimal, we divide the percentage by 100. This is because 'percent' means per hundred, so dividing by 100 gives us the equivalent decimal.

Step 3: Applying Conversion to 0.6%

Divide 0.6 by 100. When you perform the division, you get 0.006.

Step 4: Checking the Conversion

When converting 0.6% to a decimal, verify by multiplying 0.006 by 100, which should give you back 0.6%. This confirms the decimal conversion is correct.

Key Concepts

Understanding Percentages

Percentages are essential for expressing numbers as parts of a whole. The term "percent" originates from the Latin phrase _per centum_, which translates to "by the hundred."
Understanding percentages is vital for interpreting data, calculating discounts, and understanding statistics. When you see 0.6%, it indicates 0.6 parts out of a total of 100 parts.

• Percentages are used in everyday life, such as in sales to denote price reductions.
• They help in comparing proportions between different data sets.

Whenever you want to interpret percentages accurately, always think in terms of parts per hundred. This fundamental understanding sets the base for more advanced calculations and conversions, like moving from percentages to decimals.

Decimal Conversion Process

Converting percentages into decimals is a straightforward process once you grasp the concept.
The conversion involves dividing the percentage value by 100 since percentages represent the value per hundred.

• Begin with the percentage, such as 0.6%.
• Divide this value by 100 to shift the decimal point two places to the left.
• Therefore, 0.6% becomes 0.006 as a decimal.

This conversion is crucial as decimals are often more convenient to use in mathematical calculations than percentages. Converting percentages to decimals allows for easier operations in science, finance, and many real-world applications.

Mathematics Foundations

An understanding of basic mathematics lays the groundwork for tackling more complex problems later.
Percentages and decimals are among these foundational elements. Knowing how to convert between these forms is critical for mathematical literacy.

• Mathematical foundations involve understanding basic operations such as addition, subtraction, multiplication, and division.
• Knowing why each step in a conversion is necessary helps build analytical reasoning skills.
• This understanding also aids in solving algebraic equations and other quantitative problems efficiently.

Firm grasp of these foundational concepts empowers students to approach higher-level mathematics with confidence. Mathematically literate individuals can critically analyze data, solve real-world problems, and successfully engage in fields like engineering or finance.