Math Problem Statement

Convert the following decimal to a fraction, 75.952

Question 7 options:

75 95.2/100

75 9.52/10

75952/1000

75 952/1000

all of the choices

Solution

To convert the decimal 75.952 to a fraction, follow these steps:

  1. Separate the whole number from the decimal part:

    • Whole number: 75
    • Decimal part: 0.952
  2. Convert the decimal part (0.952) to a fraction:

    • 0.952 = 952/1000 because there are three decimal places.
  3. Combine the whole number with the fraction: 75.952=75+952100075.952 = 75 + \frac{952}{1000}

  4. Now, express this as a single fraction: 75.952=75×1000+9521000=75000+9521000=75952100075.952 = \frac{75 \times 1000 + 952}{1000} = \frac{75000 + 952}{1000} = \frac{75952}{1000}

So, the correct answer is:
75952/1000

This matches the option: 75952/1000

Do you have any questions or need further clarification? Here are five related questions to deepen your understanding:

  1. How do you simplify a fraction if needed?
  2. Can every decimal be converted into a fraction? Why or why not?
  3. How would you convert 75.952 into a mixed number?
  4. What is the process for converting repeating decimals into fractions?
  5. How would you handle converting a large decimal number with more than three decimal places?

Tip: When converting a decimal to a fraction, the number of decimal places determines the power of 10 in the denominator.

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Math Problem Analysis

Mathematical Concepts

Decimal Conversion
Fractions
Place Value

Formulas

Decimal to Fraction Conversion: (Decimal Part) / (Power of 10 based on number of decimal places)
Whole Number and Fraction Combination: Whole Number + (Fraction)

Theorems

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Suitable Grade Level

Grades 6-8