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Chapter 5: Problem 226

Order each pair of numbers, using \(<\) or \(>\) \(\frac{3}{5}\) ___ \(0.35\)

Short Answer

Expert verified
\frac{3}{5} > 0.35

Step by step solution

01

Convert the Fraction to Decimal

Convert the fraction \(\frac{3}{5}\) to its decimal form. To do this, divide 3 by 5: \( \frac{3}{5} = 0.6 \)
02

Compare the Decimals

Compare the decimal value obtained from the fraction \(\frac{3}{5} = 0.6\) with the given decimal 0.35.
03

Determine the Correct Inequality

Since 0.6 is greater than 0.35, we can write \( 0.6 > 0.35 \). Therefore, \(\frac{3}{5}\) is greater than 0.35.

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Key Concepts

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

Converting fractions to decimals
One important skill in math is converting fractions to decimals. This allows us to compare them easily with other numbers. To convert a fraction like \(\frac{3}{5}\), we divide the numerator (top number) by the denominator (bottom number). So, \(\frac{3}{5}\) means we divide 3 by 5. This gives us 0.6.
It's often useful to have decimals instead of fractions for comparison purposes, especially when dealing with inequalities or solving problems.
Remember, when converting fractions:
  • Identify the numerator and denominator.
  • Divide the numerator by the denominator.
  • Write down the decimal result.
Using these steps ensures you can accurately convert any fraction to its decimal form.
Inequalities
Inequalities are used to show that one number is larger or smaller than another. Common symbols include \(>\) for 'greater than' and \(<\) for 'less than'. To understand inequalities, it's essential to be comfortable with comparing both fractions and decimals.
In our example, we had to determine if \(\frac{3}{5}\) was greater or smaller than 0.35. After converting \(\frac{3}{5}\) to 0.6, it was clear that 0.6 is greater than 0.35. So we use the 'greater than' symbol.
Key points about inequalities:
  • Convert numbers to the same form (both decimals or both fractions).
  • Use the right symbol to show the relationship.
  • Double-check your conversion and comparison to avoid mistakes.
Mastering inequalities helps solve a variety of math problems and understand relationships between numbers.
Decimal comparison
Comparing decimals involves looking at each digit from left to right. Start by comparing digits in the same place value, such as the tenths or hundredths.
In our example, we compared 0.6 and 0.35.
Here's a guide for decimal comparison:
  • Align the numbers by the decimal point.
  • Compare digits in each place value.
  • Decide which number is larger based on the first differing digit from left to right.
So, since 0.6 (six tenths) is bigger than 0.35 (thirty-five hundredths), 0.6 is greater.
Decimal comparison is essential for solving inequalities and understanding numerical relationships. Practice it regularly to improve your confidence and accuracy with numbers.

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