key term - Decimal Fraction

Definition

A decimal fraction is a type of fraction where the denominator is a power of 10, allowing the number to be expressed using digits to the right of a decimal point. Decimal fractions are a convenient way to represent quantities that are not whole numbers.

5 Must Know Facts For Your Next Test

1. Decimal fractions can be converted to and from common fractions by writing the numerator as the digits to the right of the decimal point and the denominator as a power of 10.
2. Decimal fractions allow for precise representation of quantities and are commonly used in measurements, calculations, and financial applications.
3. The place value of digits in a decimal fraction corresponds to powers of 10, with the digits to the right of the decimal point representing tenths, hundredths, thousandths, and so on.
4. Decimal fractions can be added, subtracted, multiplied, and divided using the same rules as whole numbers, with the decimal point aligning during the operations.
5. Rounding decimal fractions to a specified number of decimal places or significant figures is a common practice to simplify calculations and express values with appropriate precision.

Review Questions

• Explain how to convert a common fraction to a decimal fraction.
  • To convert a common fraction to a decimal fraction, divide the numerator by the denominator. The resulting quotient will be the decimal representation of the fraction. For example, to convert the fraction 1/4 to a decimal fraction, divide 1 by 4, which gives 0.25. The decimal fraction 0.25 is equivalent to the common fraction 1/4.
• Describe the relationship between the place value of digits in a decimal fraction and powers of 10.
  • In a decimal fraction, the place value of digits to the right of the decimal point corresponds to powers of 10. The rightmost digit represents tenths (10^-1), the next digit represents hundredths (10^-2), the digit after that represents thousandths (10^-3), and so on. This allows for precise representation of quantities less than one, with the place value of each digit indicating the magnitude of the fraction.
• Analyze the process of rounding a decimal fraction to a specified number of decimal places and explain its importance.
  • Rounding a decimal fraction to a specified number of decimal places involves determining the appropriate value to assign to the digits after the desired decimal place. This is important for simplifying calculations, expressing values with appropriate precision, and ensuring consistency in measurements and data analysis. Rounding can be done by examining the digit in the next decimal place and either keeping the current digit or adjusting it up or down based on established rounding rules. Proper rounding is crucial in many real-world applications, such as scientific research, engineering, and finance, where precise representation of quantities is essential.

Related terms

Fraction:

A mathematical representation of a part of a whole, expressed as a ratio of two numbers.

Decimal:

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

Terminating Decimal:

A decimal that has a finite number of digits, meaning it can be expressed as a simple fraction.