Decimal to Fraction Conversion

Definition

Decimal to fraction conversion is the process of expressing a decimal number as an equivalent fraction. This is an important skill in the context of working with fractions, as it allows for the seamless transition between decimal and fractional representations of quantities.

5 Must Know Facts For Your Next Test

1. Decimal to fraction conversion is achieved by finding the appropriate numerator and denominator that represent the decimal value.
2. Terminating decimals can be easily converted to fractions by identifying the place value of the last non-zero digit and using that as the denominator.
3. Repeating decimals can be converted to fractions by identifying the pattern of the repeating digits and using that to construct the numerator and denominator.
4. The conversion process often involves simplifying the resulting fraction to its lowest terms.
5. Decimal to fraction conversion is a fundamental skill in working with fractions and is necessary for understanding the relationship between decimal and fractional representations.

Review Questions

• Explain the process of converting a terminating decimal to a fraction.
  • To convert a terminating decimal to a fraction, first identify the place value of the last non-zero digit. This place value will become the denominator of the fraction. Then, multiply the decimal by the appropriate power of 10 to move the decimal point to the right, creating the numerator. Finally, simplify the fraction by dividing both the numerator and denominator by any common factors to obtain the simplified fraction.
• Describe the process of converting a repeating decimal to a fraction.
  • To convert a repeating decimal to a fraction, first identify the pattern of the repeating digits. Multiply the original decimal by the appropriate power of 10 to move the decimal point to the right, creating the numerator. Then, subtract the original decimal from the new value to isolate the repeating portion, which becomes the denominator. Finally, simplify the fraction by dividing both the numerator and denominator by any common factors.
• Analyze the relationship between decimal and fractional representations, and explain how decimal to fraction conversion can be used to better understand the properties of fractions.
  • Decimal and fractional representations are closely related, as they both express the same underlying quantity. By converting between decimal and fractional forms, students can gain a deeper understanding of the properties of fractions, such as equivalence, simplification, and operations. The conversion process highlights the connection between the decimal and fractional systems, allowing students to see how the same value can be expressed in different ways. This understanding is crucial for developing fluency with fractions and their applications in mathematics.

Related terms

Fraction:

A fraction is a numerical quantity that represents a part of a whole, expressed as a ratio of two integers, the numerator and the denominator.

Decimal: A decimal is a numerical representation that uses a decimal point to express a quantity that is not a whole number, allowing for the representation of fractional parts.

Terminating Decimal:

A terminating decimal is a decimal that has a finite number of digits after the decimal point, and can be expressed as a simple fraction.