Problem 67 - Algebra A Combined Function

Question

Write each percent as \(a\) decimal. $$ 96.55 \% $$

Step-by-Step Solution

Answer

96.55% as a decimal is 0.9655.

Step 1: Understand the Problem

We need to convert the percentage 96.55% into its decimal form. Remember, a percentage is a number given out of 100.

Step 2: Convert Percentage to Fraction

First, express the percentage as a fraction. Since percentages are out of 100, write 96.55% as \( \frac{96.55}{100} \).

Step 3: Simplify the Fraction to a Decimal

To convert the fraction \( \frac{96.55}{100} \) to a decimal, we divide 96.55 by 100.

Step 4: Perform the Division

Divide 96.55 by 100, which yields 0.9655. This operation moves the decimal point two places to the left.

Key Concepts

Percentage Conversion

Converting a percentage into another format is a basic yet essential mathematical skill. Here’s how you can easily convert a percentage to a decimal:

• Understand that a percentage is a number expressed as a fraction of 100. So, when you have a percentage, it represents the part-per-hundred.
• To convert a percentage to a decimal, you'll need to turn the percentage into a fraction over 100. For example, with 96.55%, this is written as \( \frac{96.55}{100} \).
• This fraction conversion is the same for any percentage you encounter, making it a straightforward process each time.

After converting into a fraction, the next step is translating that into a decimal.

Decimal Representation

Decimal representation is a way to express fractions using base ten. It is a standardized format that is easy to read and compute with:

• Once you've converted a percentage to a fraction like \( \frac{96.55}{100} \), the next step is transforming that fraction into a decimal.
• The denominator of 100 in the fraction indicates that you should move the decimal point two places to the left in the numerator. This operation directly correlates to dividing the number by 100.
• Perform this operation to shift 96.55 two places left to get 0.9655. This is the decimal form of the percentage 96.55%.

Understanding decimals is crucial because it simplifies comparisons, calculations, and makes them more intuitive.

Mathematical Operations

Mathematical operations such as division play a key role in converting percentages to decimals.

• The fundamental operation involved in conversion is division. You divide the percentage by 100, effectively moving the decimal point two places to the left.
• For example, with 96.55, dividing by 100 simplifies to moving the decimal point left, resulting in 0.9655, which is your decimal.
• This operation requires basic skills in division, which is moving the decimal part and executing precise numerical adjustment.

Mastering these operations enhances your numerical fluency and prepares you for more complex calculations.