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Chapter 10: Problem 18

Convert to decimal notation. $$ \frac{1}{4} $$

Short Answer

Expert verified
0.25

Step by step solution

01

Understand the Fraction

The given fraction is \(\frac{1}{4}\). This fraction represents 1 part out of 4 equal parts.
02

Convert the Fraction to Decimal

To convert \(\frac{1}{4}\) to a decimal, divide the numerator (1) by the denominator (4). This gives us 0.25.

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Key Concepts

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

Fraction to Decimal Conversion
When converting a fraction to a decimal, the goal is to turn the fractional value into a format that uses base 10. A fraction consists of a numerator and a denominator. To convert \( \frac{1}{4} \) into a decimal, divide the numerator (1) by the denominator (4). This means you'll perform the division 1 梅 4 = 0.25.
  • The result, 0.25, is the decimal equivalent of the fraction \( \frac{1}{4} \).
  • This process can be used for any fraction.
  • The key is to focus on the division operation, allowing for a simple and straightforward conversion.

When performing this conversion, it's helpful to understand your tools like calculators, which can make the division quick and error-free.
Numerator and Denominator
A fraction is made up of two parts: the numerator and the denominator. These two numbers are crucial in understanding and working with fractions.
  • **Numerator**: The top number of a fraction. Represents how many parts we have or are considering.
  • **Denominator**: The bottom number of a fraction. Indicates the total number of equal parts into which the whole is divided.
So, for the fraction \( \frac{1}{4} \), the numerator (1) tells us that we have one part, and the denominator (4) signifies that the whole is divided into four equal parts.
When converting fractions to decimals:
1. **Divide the numerator by the denominator**: For \( \frac{1}{4} \), you divide 1 by 4 to get 0.25.
2. **Understand the division process**: The division might not always be straightforward, especially with more complex fractions. But focusing on simple ones helps to build up confidence.
Understanding Place Value
In decimal notation, each digit has a place value, depending on its position relative to the decimal point.
**Example with 0.25**:
  • **0**: This is the unit place (or ones place).
  • **2**: This is in the tenths place.
  • **5**: This is in the hundredths place.
Therefore, 0.25 reads as 'zero point two five'. The '2' is in the tenths place, and the '5' is in the hundredths place, together, they make 25 hundredths.
Understanding place value is vital, as it helps in reading, writing, and converting decimals to fractions and vice versa.

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