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Chapter 2: Problem 21

Replace the box \(\square\) with \(<\) or \(>\) to make a true statement. $$4.5 \square 0.45$$

Short Answer

Expert verified
4.5 > 0.45

Step by step solution

01

Understand the Problem

We need to determine whether 4.5 is less than or greater than 0.45 and replace the box \(\square\) with the correct inequality sign.
02

Express the Numbers Differently

To easily compare the numbers, express 4.5 and 0.45 using the same representation by decimal or fraction.
03

Compare Whole Numbers and Decimal Values

Both numbers are decimals. Note that 4.5 is greater than 0.45 because 4.5 has a larger whole number part compared to 0.45.
04

Conclusion

Since 4.5 is a larger number than 0.45, we replace \(\square\) with \(>\), making the statement \(4.5 > 0.45\) true.

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Key Concepts

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

Decimal Comparison
Comparing decimal numbers involves understanding which one is larger or smaller based on their digits. This process might seem challenging initially, but it follows some straightforward steps:
  • Start by comparing the digits from left to right.
  • First, check the whole number part before the decimal point. The number with a larger whole part is greater.
  • If the whole numbers are the same, compare digits after the decimal point similarly.

For instance, in the exercise given, when comparing 4.5 and 0.45, it's evident that 4.5 is greater because 4 is larger than 0.
In practice, ensuring both numbers have the same number of decimal places can make comparisons easier. Pad the shorter decimal with zeroes, and align the numbers carefully.
Number Representation
Numbers can be represented in numerous ways, and how they're expressed can greatly aid in solving mathematical problems. For instance:
  • Decimal Form: Numbers expressed with digits and a decimal point, such as 4.5.
  • Fractional Form: Numbers represented as one number over another, like 9/2 for 4.5.
  • Percentage: Expressing decimals as parts of 100, such as 450% for 4.5.

In math problems like the one in the exercise, converting both numbers to a common form, like decimals, can simplify the process of comparison and problem-solving.
Remember, always choose the form that makes calculations straightforward and aligning numbers effortless.
Math Problem Solving
Solving math problems such as inequalities requires a systematic approach. Breaking the process into distinct steps can simplify complex problems. Here鈥檚 a basic method you can follow:
  • Understand the Problem: Clearly define what is being asked. In this case, determine which inequality sign makes the statement true.
  • Choose a Strategy: Decide whether to compare numbers in their current form or convert them to a more familiar form, like fractions or decimals.
  • Execute the Solution: Compare the numbers step by step. Validate your answer by checking it thoroughly.
  • Review and Conclude: Analyze if your solution makes logical sense, then finalize your answer.

This structured approach not only helps solve the problem at hand but also builds a strong problem-solving skill set for tackling different mathematical challenges.

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Most popular questions from this chapter

Consider the formula $$\frac{0.55-p}{\sqrt{\frac{p(1-p)}{n}}}$$ Evaluate this expression using the given values. Round the results to three decimal places. $$p=0.54, n=20$$

Consider a variable \(r\) where \(r\) represents the whole numbers from 1 to 15. Stated mathematically, the possible values of \(r\) are $$r=1,2, \ldots, 14,15$$ Determine which values satisfy the given compound inequalities. $$5

Solve the equations. More than one step is needed in each case.$$-3-4 x=-47$$

Consider the formula $$\frac{x-50}{\frac{s}{\sqrt{n}}}$$ Evaluate this expression using the given values. Round the results to two decimal places. $$x=36.9, s=9.3, n=19$$

Simplify the expressions, which involve exponents and square roots. Round the results to two decimal places as necessary. $$\frac{(2.33)^{2} \cdot 0.25}{0.015^{2}}$$
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