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Chapter 4: Problem 50

Which number is larger? $$ \frac{73}{10}, 0.73 $$

Short Answer

Expert verified
The number \(\frac{73}{10}\) is larger.

Step by step solution

01

Convert Fraction to Decimal

Convert the fraction \(\frac{73}{10}\) to a decimal form. Divide 73 by 10: \(\frac{73}{10} = 7.3\)
02

Compare Decimals

Compare the decimal value 7.3 with 0.73. Notice that 7.3 has a whole number part which is significantly larger than the decimal 0.73.
03

Determine Larger Number

Since 7.3 is greater than 0.73, determine that \(\frac{73}{10}\) is larger.

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Key Concepts

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

Decimal Conversion
When comparing fractions and decimals, one of the first steps is often to convert all values to the same format. This makes it easier to see which is larger. For instance, let鈥檚 take the fraction \(\frac{73}{10}\). To convert this fraction to a decimal, you divide the numerator (73) by the denominator (10).
When you do the division: \(73 \div 10 = 7.3\).
This simple division is the essence of converting fractions to decimals.
  • Numerator: The top number of the fraction (73 in this case).
  • Denominator: The bottom number of the fraction (10 here).
  • Division: 73 divided by 10 equals 7.3.
By converting \(\frac{73}{10}\) into 7.3, we have the decimal form, making comparison straightforward.
Fraction Comparison
After conversion of the fraction to a decimal, comparing values becomes simpler.
Let鈥檚 consider the two numbers we have: 7.3 and 0.73.
Here are key points to remember when comparing decimals:
  • Whole Number: Examine the whole number part first. For 7.3, the whole number part is 7, and for 0.73, it鈥檚 0. Clearly, 7 is greater than 0.
  • Decimal Part: If needed, compare digits after the decimal point. For example, if we had to compare 1.5 with 1.54: First, look at the whole number (both are 1), then look at the first decimal (both are 5), and finally compare the next decimal digit (0 vs 4), making 1.54 greater than 1.5.
In our case, since 7.3 has a whole number part that is larger than the whole number part of 0.73, we can clearly see that 7.3 (or \(\frac{73}{10}\)) is the larger number.
Steps for Comparison
Here is a simple step-by-step process to compare a fraction and a decimal:
  • Step 1: Convert Fraction to Decimal
    Start by converting the fraction to a decimal. For \(\frac{73}{10}\), this meant dividing 73 by 10, resulting in 7.3.
  • Step 2: Compare Values
    Compare the decimal forms. Look at the whole number part first, and if necessary, the decimal part next. In our example, we compared 7.3 and 0.73 by first looking at the whole number parts (7 and 0).
  • Step 3: Determine the Larger Number
    Identify the larger value based on the comparison. Since 7.3 has a larger whole number part compared to 0.73, \(\frac{73}{10}\) is determined to be larger.
Remember, converting fractions to decimals puts them in the same format, which simplifies the comparison process significantly. Practice with more examples to become comfortable with these steps!

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