Problem 93 - Algebra 1: Concepts and Skills

Question

Complete the statement using \(<,>,\) or \(=.\) $$ 0.66 ? 60 \% $$

Step-by-Step Solution

Answer

The solution to the exercise is \(0.66 > 60 %\).

Step 1: Convert Percentage to Decimal

In order to compare the values, the percentage value has to be converted into a decimal. This conversion can be done by dividing the percentage value by 100. Hence, \[ 60 \% = \frac{60}{100} = 0.6\]

Step 2: Compare Decimal Values

Now we can compare the two decimal values. This comparison will involve filling in the symbol that correctly describes the relationship between 0.66 and 0.6. When comparing, it is clear that 0.66 is more than 0.6.

Key Concepts

Decimals

Decimals are a way of representing numbers that have parts smaller than a whole. They are often made up of digits following a decimal point. For example, in the number 0.66, the digits after the decimal point show parts of one whole. Here, the six in the tenths place means 6 tenths and the six in the hundredths place means 6 hundredths.

Decimals help us express values in a precise way, especially in contexts where exact fractions or measurements are needed. They are vital in mathematics, allowing us to perform operations like addition, subtraction, multiplication, and division with greater accuracy.

• The first digit to the right of the decimal point represents tenths (e.g., in 0.6, it is 6 tenths).
• The second digit represents hundredths (e.g., in 0.66, it is 66 hundredths).

Understanding how to interpret decimals is fundamental when comparing numbers. As we see with 0.66, it is larger than 0.6 because 66 hundredths are more than 60 hundredths.

Percentages

Percentages are a way to express numbers as parts of a whole, specifically out of 100. This means every percentage is really a fraction with a denominator of 100. For instance, 60% represents 60 out of 100, or simply 0.6 when converted to a decimal.

Percentages are a common way to express proportions in everyday life. They make it easier to understand comparisons and changes in quantities. You'll often see percentages when dealing with discounts, interest rates, statistics, and more.

• A percentage shows how large one number is relative to another number.
• It is widely used in finance, statistics, and various sciences.

Understanding percentages involves being aware of their equivalence to fractions and decimals, which allows easy conversion among them.

Conversion from Percentage to Decimal

Converting percentages into decimals is a straightforward process that helps in performing arithmetic operations and comparisons. The conversion involves dividing the percentage number by 100. This is because percent literally means per hundred.

For example, to convert 60% to a decimal, you divide by 100, yielding 0.6: \[60\% = \frac{60}{100} = 0.6\]This process allows quick and easy comparisons between decimals and converted percentages.

• Simplifies arithmetic operations and calculations.
• Makes it easier to compare different quantities.
• Helps in solving problems like the one with 0.66 and 60%.

By converting percentages to decimals, you lose none of the original value but instead make precise calculations possible.