Problem 45 - Algebra 1: Concepts and Skills

Question

Complete the statement using \(<,>,\) or \(=\). \(54 \% ? 0.54\)

Step-by-Step Solution

Answer

Therefore, the correct completion of the statement is \(54 \% = 0.54\).

Step 1: Convert the Percentage to Decimal

Convert the given percentage into a decimal. The conversion of a percentage into a decimal involves dividing the percentage value by 100. Therefore, we take 54 and divide it by 100 to get 0.54.

Step 2: Compare the Values

Compare the decimal obtained from Step 1 with the decimal provided in the exercise, 0.54.

Step 3: Choose the Correct Symbol

From the comparison made, if both values are equal, then the symbol would be '='. If the converted value is less then symbol would be '<'. If the converted value is more, then symbol is '>'. As both are equal in this case, we choose '='.

Key Concepts

Convert Percentage to Decimal

Converting a percentage to a decimal is a straightforward process and can be quite handy in various mathematical scenarios. A percentage is a way of expressing a number as a fraction of 100, so the term 'percent' means 'per hundred'. Here's how you can convert it:

• Take the given percentage value.
• Divide the number by 100.

For example, if you have 54%, you divide 54 by 100, which is equal to 0.54. Remember to move the decimal point two places to the left as a shortcut. So, 54% becomes 0.54 when converted to a decimal.
This method ensures you correctly transform percentages to decimals, which are often more practical in calculations.

Decimal Comparison

When comparing decimals, it's important to evaluate the value represented by each number carefully. Here’s how to effectively compare them:

• Line up the numbers by their decimal points.
• Start comparing from the leftmost digit.

Compare digit by digit, moving rightwards, until you find a difference. If the decimal numbers are already identical, like in our case where 0.54 is compared to another 0.54, they are equal.
Consider small differences. For instance, 0.54 is less than 0.55 because after comparing the first two identical digits (5 and 4), the last digit makes the difference. Always employ '<', '>', or '=' depending on whether the first is smaller, larger, or equal to the second decimal value, respectively.

Percentage Conversion

Converting decimals back to percentages can help in interpreting data and values more intuitively. Just as converting from percentages to decimals involves division by 100, converting back involves multiplication by 100.

• Take the decimal number you have.
• Multiply it by 100 to convert it back to a percentage.

This simple multiplication process shifts the decimal point two places to the right. Using our previous example, converting 0.54 to a percentage involves calculating 0.54 multiplied by 100, which equals 54%.
This conversion is often used when you want to express an answer in a more familiar percentage form. It's especially handy in fields like finance, statistics, and anywhere comparisons are typically made in percentages.