key term - Decimal to Fraction

Definition

Decimal to fraction is the process of converting a decimal number into an equivalent fraction. This is an important skill in intermediate algebra, as it allows for the manipulation and simplification of numerical expressions that contain both decimal and fractional components.

5 Must Know Facts For Your Next Test

1. The denominator of the equivalent fraction is determined by the number of decimal places in the original decimal number.
2. To convert a decimal to a fraction, the decimal number is written as the numerator, and the denominator is a power of 10 equal to the number of decimal places.
3. Repeating decimals can be converted to fractions by identifying the pattern and using a formula to determine the numerator and denominator.
4. Terminating decimals, where the decimal expansion ends, can be easily converted to fractions by writing the decimal as the numerator and a power of 10 as the denominator.
5. Converting between decimal and fraction forms is a fundamental skill in algebra, as it allows for the manipulation and simplification of expressions containing both decimal and fractional components.

Review Questions

• Explain the process of converting a decimal number to a fraction.
  • To convert a decimal number to a fraction, the decimal is written as the numerator, and the denominator is a power of 10 equal to the number of decimal places in the original decimal. For example, the decimal 0.375 would be converted to the fraction 375/1000, as the decimal has 3 decimal places. This process allows for the manipulation of numerical expressions that contain both decimal and fractional components.
• Describe how the conversion of a repeating decimal to a fraction differs from a terminating decimal.
  • The conversion of a repeating decimal to a fraction involves identifying the repeating pattern and using a formula to determine the numerator and denominator. For example, the repeating decimal 0.3333... can be converted to the fraction 1/3. In contrast, a terminating decimal, where the decimal expansion ends, can be easily converted to a fraction by writing the decimal as the numerator and a power of 10 as the denominator. The key difference is that repeating decimals require a more complex process to determine the equivalent fraction.
• Analyze the importance of being able to convert between decimal and fraction forms in intermediate algebra.
  • The ability to convert between decimal and fraction forms is crucial in intermediate algebra, as it allows for the manipulation and simplification of numerical expressions that contain both decimal and fractional components. This skill is essential for solving equations, simplifying algebraic expressions, and working with various mathematical concepts that involve the interplay between decimals and fractions. By mastering the conversion process, students can more effectively navigate the complexities of intermediate algebra and develop a deeper understanding of the relationships between different numerical representations.

Related terms

Decimal: A number written in the base-10 numeral system, using digits 0-9 and a decimal point to represent values less than one.

Fraction:

A numerical representation of a part of a whole, expressed as a ratio of two integers, the numerator and denominator.

Place Value:

The value of a digit in a number based on its position relative to the decimal point.