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Chapter 6: Problem 70

Insert \(<\) or \(>\) to form a true statement. $$ 7.26 \quad 7.026 $$

Short Answer

Expert verified
7.26 > 7.026

Step by step solution

01

Compare the Whole Numbers

Both numbers have the same whole number part: 7.
02

Compare the Tenths Digit

The tenths digit of 7.26 is 2, while the tenths digit of 7.026 is 0. Since 2 is greater than 0, 7.26 is greater than 7.026.
03

Form the True Statement

Based on the analysis, the true statement is: \( 7.26 > 7.026 \).

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Key Concepts

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

Understanding Decimal Place Value
Decimals use place values to represent numbers less than a whole. Understanding decimal place value is crucial when comparing numbers.
The place value in decimals works similarly to whole numbers but extends into smaller units:
  • First, we have the whole number part, which is to the left of the decimal point.
  • Directly after the decimal point, the first digit is in the tenths place, representing one-tenth of a whole.
  • The next digit is in the hundredths place, representing one-hundredth of a whole, and so on.
For example, in the number 7.26, the digit 2 is in the tenths place, and the digit 6 is in the hundredths place.
Recognizing these place values helps in accurately determining the size of a decimal number.
Techniques for Number Comparison
When comparing decimals, follow step-by-step techniques to clearly see which number is larger. Start by looking at the whole numbers.
If they are the same, move to the tenths place, then the hundredths, and further if needed:
  • Compare the whole number parts first; if one number has a larger whole number, it is greater.
  • If whole numbers are equal, compare the tenths digit; a larger digit means a greater number.
  • If the tenths are equal, proceed to the hundredths, then thousandths, etc., until a difference is found.
The systematic comparison is useful when numbers are close. It's much like comparing apples in size, only now we are focusing on their decimal extent.
This method assures you'll always identify the correct relationship between two decimals.
Interpreting Mathematical Inequalities
Mathematical inequalities are symbols that show the relative size or order of two numbers. Commonly used signs include:
  • ">" (greater than)
  • "<" (less than)
  • "=" (equal to)
In our exercise, we determine which sign to use by following the comparison process based on place value. If one number is larger, use ">"; if smaller, use "<".
For instance, when comparing 7.26 and 7.026, we recognize through place value that 7.26 is greater, thus, we use the inequality sign to write:
\[ 7.26 > 7.026 \] Understanding these symbols helps mathematically express the relationship between different numbers.
It makes solving numeric problems clear and structured.

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Most popular questions from this chapter

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Without using a calculator, explain how you know that \(\sqrt{27}\) is not approximately 3.296 .

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Describe a situation in which writing a proportion might solve a problem related to driving a car.

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