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Chapter 6: Problem 50

Use \(<\) or \(>\) to make a true statement. $$153.77 ? 153.707$$

Short Answer

Expert verified
Answer: 153.77 is greater than 153.707.

Step by step solution

01

Compare Whole Number Parts

We will start by comparing the whole number parts, which are 153 for both numbers. Since they are equal, we will move on to comparing the decimal parts.
02

Compare Tenths Place

Now we look at the tenths place in both numbers: 0.07 for the first number (153.77) and 0.007 for the second number (153.707). Clearly, 0.07 is greater than 0.007, so we can make a conclusion.
03

Write the Inequality

Since the first number, 153.77, has a greater tenth place value (0.07) than the second number, 153.707 (0.007), we conclude that 153.77 is greater than 153.707. Therefore, the true inequality statement is: $$153.77 > 153.707$$

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Key Concepts

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

Inequalities
Understanding inequalities is fundamental in comparing numbers and their values. An inequality is a mathematical expression that shows the relationship between two values that are not equal. In the context of decimal numbers, using '<' means 'is less than' and '>' means 'is greater than'. When comparing two decimal numbers, the inequality sign shows which number is larger. The correct use of inequality signs is crucial, as it conveys precise mathematical meaning. For example, stating that 153.77 > 153.707, expresses that 153.77 is greater than 153.707, showcasing an important mathematical relationship between the two numbers.
Whole Number Comparison
Whole number comparison lays the groundwork for comparing decimal numbers. This is the very first step in our mathematical reasoning process. Comparing the whole number parts of two decimals is straightforward: if they are not the same, the larger whole number indicates the larger decimal. However, in cases where the whole number parts are identical, like with 153.77 and 153.707, we don't stop there. We proceed to compare the numbers place-by-place following the decimal point to determine which is larger.
Decimal Places
Decimal places play a pivotal role when whole numbers are identical. They are the numbers that come after the decimal point, and they represent fractions of a whole. Each position after the decimal point has a specific place value: tenths, hundredths, thousandths, and so forth. In comparing 153.77 and 153.707, even though the numbers before the decimal are the same, the differing digits in the tenths and hundredths places determine which number is larger. This system allows for precise comparisons and exactitude in numerical expressions.
Mathematical Reasoning
Mathematical reasoning involves logical thinking to figure out the relationship between different numbers. With this skill, students can compare decimal numbers step by step. After comparing whole numbers and finding them equal, mathematical reasoning guides us to step through each decimal place, ensuring no value is overlooked. Like a detective looking for clues, each step in comparing 153.77 to 153.707 requires careful observation and thought. From whole numbers to the smallest decimal place, mathematical reasoning is our reliable tool for determining numerical relationships and solving inequalities.

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Most popular questions from this chapter

Evaluate each expression using the given values. $$v t+\frac{1}{2} a t^{2} ; v=20, t=0.6, a=-12.5$$

For Exercises \(71-76,\) use 3.14 to approximate \(\pi\). To manufacture a light fixture, a company bends 6.5 feet of metal tubing into a circle. What is the radius of this circle?

Add or subtract. $$\left(20.5 m^{4}+16 m^{2}-18.3 m-0.77\right)+\left(0.9 m^{4}-2.08 m^{2}+1\right)$$

Solve. The closing price of a stock one day was 35.25 dollar. The next day the closing price of the same stock was 32.50 dollar. Let \(n\) represent the amount the stock's closing price changed. Write an equation that can be used to find the amount the closing price changed; then solve the equation.

Solve and check. $$m+3.67=14.5$$
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