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Chapter 4: Problem 36

Write decimal notation. $$ 4 \frac{67}{1000} $$

Short Answer

Expert verified
4.067

Step by step solution

01

Understand the Mixed Fraction

The given mixed fraction is \(4 \frac{67}{1000}\). It consists of a whole number part (4) and a fractional part (\(\frac{67}{1000}\)).
02

Convert the Fractional Part to Decimal

To convert \(\frac{67}{1000}\) to decimal form, note that the denominator is 1000, so each digit in the numerator represents a tenth, hundredth, or thousandth. Therefore, \(\frac{67}{1000} = 0.067\).
03

Combine Whole Number and Decimal

Now combine the whole number part (4) with the decimal fraction obtained (0.067). Therefore, \(4 \frac{67}{1000} = 4 + 0.067 = 4.067\).

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Key Concepts

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

Mixed Fraction
A mixed fraction is a combination of a whole number and a proper fraction. For example, in \( 4 \frac{67}{1000} \), the number 4 is the whole number part, and \( \frac{67}{1000} \) is the fractional part. Mixed fractions are useful when you need to represent quantities greater than 1 in a more compact form. To fully understand mixed fractions, always identify the whole number part and the fractional part separately before doing any conversion.
Fractions to Decimals
Converting fractions to decimals is essential in many real-world applications. To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). For example, with \( \frac{67}{1000} \), you divide 67 by 1000 to get 0.067.
Knowing the place value is crucial:
  • 10s place: tenths (0.1)
  • 100s place: hundredths (0.01)
  • 1000s place: thousandths (0.001)
This method helps in achieving accurate decimal representations of fractions.
Math Conversion Steps
Follow these simple steps to convert mixed fractions to decimals:
1. Identify the whole number and the fraction part from the mixed fraction. For example, in \( 4 \frac{67}{1000} \), 4 is the whole number, and \( \frac{67}{1000} \) is the fraction.
2. Convert the fraction part to a decimal by dividing the numerator by the denominator. Here, \( \frac{67}{1000} = 0.067 \).
3. Finally, add the whole number to the fraction's decimal form. Therefore, \( 4 + 0.067 = 4.067 \).
Remember, practice these steps with different examples to get comfortable with mixed fraction to decimal conversions.

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