Problem 57 - Algebra 1: Concepts and Skills

Question

Compare using \(<,>,\) or \(=\) \(5 \% ? 0.05\)

Step-by-Step Solution

Answer

\(5\% = 0.05\)

Step 1: Convert Percentage to Decimal

To convert a percentage into a decimal, we divide the percentage by 100. So, here, 5% becomes \(5 ÷ 100 = 0.05\)

Step 2: Compare the Decimal Values

Next, compare these two decimal values 0.05 and 0.05.

Step 3: Assign the Correct Comparison Symbol

As the two decimal values are equal, the correct comparison symbol will be '='. So, \(5\% = 0.05\).

Key Concepts

Percentage Conversion

Converting percentages to decimals is a key math skill that simplifies many calculations. It involves dividing the percentage value by 100. This mathematical maneuver transforms the percentage into a decimal format, making it easier to compare or perform further operations.
For example, let's look at 5%. To convert it to a decimal, you divide 5 by 100, resulting in 0.05.
So for 5%, \[5\% = \frac{5}{100} = 0.05\]

• This conversion is necessary because percentages are based on fractions out of 100.
• It enables easy arithmetic operations and comes in handy in various real-world applications such as calculating discounts and interest rates.

Remember, changing percentages to decimals simplifies understanding and problem-solving in mathematics.

Decimal Comparison

Comparing decimal numbers is straightforward when you understand their place values. Decimals represent fractions of whole numbers, where each place after the decimal point signifies a power of ten.
The first important step is aligning the decimal points to ensure you compare similar place values.
Take the decimals 0.05 and 0.05. Notice that both numbers have '0' in the tenths and '5' in the hundredths place, making them exactly equal.

• Line up the decimal points.
• Compare each digit from left to right.
• Identify which number has the greater or lesser value or if they are equal.

Decimal comparison is crucial, especially in contexts that require precision, like financial calculations.

Mathematical Symbols

Mathematics is full of symbols that help express relationships between numbers succinctly and effectively. The symbols <, >, and = represent comparisons between values.

• \(<\) means 'less than.'
• \(>\) means 'greater than.'
• \(=\) means 'equal to.'

In our exercise, we used the '=' symbol. This symbol indicates that both values on either side are exactly the same.
It's used in equations and comparisons where two quantities are proven to be identical.
Understanding these symbols is vital for interpreting data and solving equations in mathematics. They provide a universal language to explain the exact nature of the mathematical relations between numbers.