Problem 83 - Algebra A Combined Function

Question

Write each decimal as a percent. $$ 0.004 $$

Step-by-Step Solution

Answer

0.004 as a percent is 0.4%.

Step 1: Understanding Percent and Decimal Relationship

To convert a decimal to a percent, multiply the decimal by 100. This process is based on the fact that 'percent' means 'per hundred'. Therefore, multiplying by 100 shifts the decimal point two places to the right.

Step 2: Converting 0.004 to a Percent

Take the decimal 0.004 and multiply it by 100. Mathematically, this can be expressed as: \(0.004 \times 100\).

Step 3: Simplifying the Calculation

Perform the multiplication: \(0.004 \times 100 = 0.4\). This means that when 0.004 is converted to a percent, the result is 0.4%.

Key Concepts

Decimal Representation

Decimals are numbers expressed in a form that shows a part of a whole. They use a decimal point to separate the whole number from the fractional part. For example, in the number 0.004, the decimal point separates the zero whole number from the fractional part, which is 004. Understanding decimals is crucial because it allows us to work with numbers smaller than one, which is especially useful in fields like science, engineering, and finance.

• The number to the right of the decimal point represents tenths, hundredths, thousandths, etc., based on its position.
• In 0.004, the 4 is in the thousandths position, meaning it is equivalent to 4 parts out of 1000, or 4/1000.

It's essential to grasp this representation because it forms the basis for converting decimals to percentages, among other conversions.

Multiplication by 100

When converting a decimal to a percent, we multiply by 100. This is because a percent is essentially a fraction with a denominator of 100.

• Multiplying a number by 100 is akin to adjusting it to represent how many parts there are per hundred.
• For instance, in converting 0.004 to a percent, multiplying by 100 changes its scale.

The calculation looks like this: \[ 0.004 \times 100 = 0.4 \] This step is fundamental to percent conversion and highlights why a percent is always larger than the original decimal form when expressed as a number. Multiplying by 100 expands the number's value on the scale of 100, giving a clearer picture of its proportional size.

Decimal Point Shift

An essential part of converting decimals to percentages is shifting the decimal point. This shift is a direct result of multiplying by 100. When you multiply by 100, the decimal point moves two places to the right.

• This change occurs because each multiplication by 10 shifts the decimal one place to the right.
• So for 0.004, moving the decimal point two places results in 0.4.

The decimal shift visually represents the increased scale to 100, helping to understand the translated percentage. Remember:

• One place shift represents a multiplication by 10.
• Two places represent multiplication by 100.

Practicing this concept can make it easier to quickly get results when converting decimals to percentages.