Big Ideas Math: Modeling Real Life, Grade 8
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Exercise 25 Page 419

What type of number has repeating decimals?

Rational number

Practice makes perfect

Before we consider the given number, let's recall the various types of numbers.

  • Rational Number: A number is a rational number if it can be written in the form ab, where a and b are both integers and b≠ 0.
  • Integer: A number is an integer if it is a positive or negative counting number (or zero). All integers are also rational numbers because any number can be written as a division by one, a1.
  • Whole Number: A number is a whole number if it is a non-negative counting number. All whole numbers are also integers and rational numbers.
  • Natural Number: A number is a natural number if it is a positive counting number. All natural numbers are also whole numbers, integers, and rational numbers.
  • Irrational Number: An irrational number is a number that cannot be written in the form of a rational number. These are recognized as being non-repeating, infinite decimals.

Now, let's use these definitions to categorize our real number. 0.815 The number has repeating decimals, which means that it is a rational number.