Problem 90 - Algebra 1: Concepts and Skills

Question

Complete the statement using \(<,>,\) or \(=.\) $$ 0.9 ? 89 \% $$

Step-by-Step Solution

Answer

0.9 > 89 \%

Step 1: Conversion

Convert the percentage (89%) to a decimal. This can be done by dividing the percentage by 100. Therefore, 89% as a decimal is \( \frac{89}{100} = 0.89 \)

Step 2: Comparison

Now that both numbers are in the decimal form, they can be easily compared. Compare \(0.9\) and \(0.89\). \(0.9 > 0.89\) since \(0.9\) is larger than \(0.89\).

Key Concepts

Decimal Conversion

Decimal conversion is an essential skill to master when working with percentages. It helps us translate percentages into a more manageable numerical form. To convert a percentage to a decimal, you simply divide by 100. This is because "percent" literally means per hundred. So, if you see a percentage like 89%, you're essentially looking at the number 89 per 100.

For example, the conversion process for 89% looks like this:

• Take the number 89
• Divide by 100
• This gives you the decimal 0.89

Thus, 89% expressed as a decimal is 0.89. This simple transformation makes it easier to compare and calculate with percentages in various mathematical operations.

Percentage Comparison

Comparing percentages can be tricky if you're looking only at their percentage form. Therefore, translating them into decimals is often the way to go. As shown in the previous section, converting percentages to decimals helps to standardize values, making a direct numerical comparison more straightforward.

Once percentages are converted into decimals, you can line up the decimal points and see which number is larger, smaller, or if they are equal. In the exercise, for instance, 89% was converted to 0.89. This allows you to easily compare it with another decimal like 0.9, without any further conversion.

Always remember:

• The larger the decimal, the larger the percentage it represents.
• Zero-point-nine (0.9) is larger than zero-point-eight-nine (0.89).
• Simple subtraction can quickly reveal the difference, reinforcing which number is larger or smaller.

Number Comparison

Number comparison is a fundamental part of solving inequalities. It involves determining the relative size of two or more numbers. To compare numbers effectively, they should ideally be in the same form, as seen when decimals are used in the given exercise.

When comparing numbers like 0.9 and 0.89, the process involves looking at their digits from left to right, starting after the decimal point.

• First, consider the tenths place. In 0.9, this is 9.
• Now, look at 0.89. Here, the tenths place is 8.
• Nine is greater than eight, so 0.9 is greater than 0.89.

This straightforward method of digit-by-digit comparison can clarify inequalities in simple terms, making it easier to identify which number is greater, less than, or equal.