Decimal-to-fraction conversion

Definition

Decimal-to-fraction conversion is the process of expressing a decimal number as a fraction, allowing for easier manipulation and understanding of numerical values. This conversion is essential for comparing numbers, performing calculations, and simplifying expressions. Understanding how to convert between these two forms also reinforces the relationship between fractions and decimals, highlighting their interconnectedness in mathematics.

5 Must Know Facts For Your Next Test

1. To convert a terminating decimal to a fraction, write the decimal over 1 and multiply the numerator and denominator by 10 raised to the power of the number of decimal places.
2. For recurring decimals, use algebraic methods to derive the fraction, such as setting the decimal equal to a variable and manipulating the equation to isolate the variable.
3. The greatest common divisor (GCD) can be used to simplify fractions after conversion from decimals, making them easier to work with.
4. Decimal-to-fraction conversion helps in understanding ratios and proportions, which are foundational concepts in various areas of mathematics.
5. Understanding decimal-to-fraction conversion enhances numerical literacy, allowing for clearer communication of mathematical ideas.

Review Questions

• How can you convert a terminating decimal like 0.75 into a fraction?
  • To convert 0.75 into a fraction, you write it as \( \frac{75}{100} \) since there are two decimal places. Then, simplify this fraction by finding the greatest common divisor of 75 and 100, which is 25. Dividing both the numerator and denominator by 25 gives \( \frac{3}{4} \). Thus, 0.75 is equivalent to the fraction \( \frac{3}{4} \).
• What steps would you take to convert a recurring decimal like 0.666... into a fraction?
  • To convert 0.666... into a fraction, first set it equal to a variable, say \( x = 0.666... \). Multiply both sides by 10 to get \( 10x = 6.666... \). Next, subtract the first equation from this new equation: \( 10x - x = 6.666... - 0.666... \), resulting in \( 9x = 6 \). Finally, divide both sides by 9 to find that \( x = \frac{6}{9} \), which simplifies to \( \frac{2}{3} \).
• Evaluate the significance of decimal-to-fraction conversion in understanding mathematical concepts like ratios and proportions.
  • Decimal-to-fraction conversion plays a crucial role in understanding ratios and proportions because it allows for consistent comparison between different numerical forms. By converting decimals into fractions, one can easily see relationships between values and solve problems involving proportions with greater clarity. This understanding helps students grasp more complex mathematical ideas, as ratios are often expressed as fractions. Thus, mastering this conversion process enriches overall numerical literacy and mathematical problem-solving skills.

Related terms

Recurring Decimal: A recurring decimal is a decimal number that has one or more digits that repeat infinitely, such as 0.333... which represents the fraction \( \frac{1}{3} \).

Mixed Number: A mixed number combines a whole number and a proper fraction, such as 2 \( \frac{3}{4} \), representing the sum of the whole number and the fraction.

Simplifying Fractions: Simplifying fractions involves reducing the numerator and denominator to their smallest form, making calculations and comparisons easier.