Problem 1 Classify each equation or inequa... [FREE SOLUTION]

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Chapter 15: Problem 1

Classify each equation or inequality as true or false. $$ 2.3=2.31 $$

Short Answer

Expert verified

False

Step by step solution

Understand the Equality

Analyze the two values given in the equation. Identify the decimal parts of each number and compare them.

Compare Decimal Places

Note that the first value is 2.3 and the second value is 2.31. Compare each digit at every decimal place.

Evaluate Whether the Equation is True or False

The first number, 2.3, has one decimal place, while the second number, 2.31, has two decimal places. Since 2.3 is equivalent to 2.30, they are not the same as 2.31. Therefore, the equation is false.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

True and False Equations

Understanding true and false equations is crucial in algebra. An equation is a mathematical statement that asserts the equality of two expressions. In comparing decimals, you look at whether the numbers on both sides of the equation are identical.

In the given exercise, the equation was 2.3 = 2.31. To determine its truth value, you must compare each digit individually at their respective decimal places. If any digit differs, the equation is false. Here, 2.3 has one decimal place, while 2.31 has two.

This makes the numbers unequal, and thus, the equation is false. So, knowing how to thoroughly compare digits helps in appropriately classifying the equation as true or false.

Decimal Values

Decimals are a way to represent numbers that are not whole. They consist of a whole number part and a fractional part, separated by a decimal point. For example, 2.3 consists of a whole number part, 2, and a fractional part, 3.

When comparing decimals, evaluate each digit at corresponding decimal places, starting from the left.

In our example, 2.3 can be extended to 2.30 with an additional zero in the hundredths place. This means:

2 is equal to 2
.3 is equal to .30
.30 is not equal to .31

Evaluating Equations

Evaluating equations involves determining whether two expressions are equal. This process includes several steps:

Identifying each expression.
Comparing corresponding values and decimal places.
Checking for any differences.

For example, take the equation 2.3 = 2.31. Begin by identifying both expressions, 2.3 and 2.31.

Next, compare each place value:

Ones place: 2 vs. 2 - Equal
Tenths place: 3 vs. 3 - Equal
Hundredths place: Missing vs. 1 - Not Equal

Since every digit must match for the equation to hold true, the differing hundredths place makes it false. Evaluating equations hinges on meticulously comparing each digit in both expressions.

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91影视

Classify each equation or inequality as true or false. $$ 2.3=2.31 $$

Short Answer

Step by step solution

Understand the Equality

Compare Decimal Places

Evaluate Whether the Equation is True or False

Key Concepts

True and False Equations

Decimal Values

Evaluating Equations

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