Problem 56 - Algebra 1: Concepts and Skills

Question

Compare using \(<,>,\) or \(=\) \(0.017 ? 17 \%\)

Step-by-Step Solution

Answer

0.017 < 17%

Step 1: Analyze numbers to compare.

We are tasked with comparing two numbers: 0.017 and 17%. While they're both numbers, they're in different formats. One is a decimal and the other is a percentage.

Step 2: Convert the percentage to a decimal.

A percentage is essentially a number over 100. Thus, to convert a percentage to a decimal, divide it by 100. So, 17% is equivalent to 17/100 or 0.17.

Step 3: Compare the two numbers.

Now that we have both numbers in decimal form, we can easily compare them. 0.017 is less than 0.17. Hence, 0.017 < 17%.

Key Concepts

Decimal and Percentage Conversion

Understanding how to convert between decimals and percentages is a fundamental skill in math. A decimal represents a fraction with a denominator of 10, 100, or any higher power of 10, while a percentage is a fraction with a denominator of 100.

To convert from a percentage to a decimal, simply divide by 100. For example, with 17%, divide 17 by 100, which gives you 0.17. Conversely, to convert from a decimal to a percentage, multiply by 100. Thus, a decimal like 0.17 becomes 17%. This conversion is crucial because it allows us to compare numbers in different forms on an equal basis and solve problems effectively.

Inequalities in Math

Inequalities are mathematical expressions that describe the relative size or order of two items. They are essential in many aspects of mathematics and are represented by symbols such as < (less than), > (greater than), and = (equal to). Understanding inequalities allows us to compare numbers, functions, and even algebraic expressions to determine their relationship.

Working with inequalities involves several considerations, including the direction of the inequality sign. For instance, when multiplying or dividing by a negative number, the inequality sign flips. It's also important to know that inequalities can have multiple solutions, especially when dealing with variable expressions.

Mathematical Comparison

Comparing numbers is a basic mathematical skill that involves determining whether one number is greater than, less than, or equal to another number. In our exercise, the comparison was between a decimal and a percentage. The process of comparing begins with ensuring the numbers are in the same format, which often requires conversion.

Once the numbers are in a compatible format, look at each place value or digit and determine the relationship. With decimals, start from the left-most digit—the digits before the decimal point—and move to the right. In our example, after converting 17% to a decimal, it was clear that 0.017 is smaller than 0.17, as the second decimal place is 1 in the former and 7 in the latter, establishing 0.017 < 0.17.