olesia0131
contestada

Drag the choices into the boxes to explain how all real numbers have a decimal expansion.


The decimal forms of some real numbers, like( ), terminate, while the decimal forms of other real numbers, like( ), do not terminate, but have a repeating pattern. Still, other real numbers, like( ), have decimal forms that neither terminate nor repeat. the answer choices are, 5 squared; 3/16; 4 2/11

Respuesta :

sqdancefan

Answer:

  • terminate: 3/16
  • do not terminate: 4 2/11
  • neither terminate nor repeat: √5

Step-by-step explanation:

All rational numbers have decimal expansions that terminate or repeat. The number will have a repeating decimal expansion if its equivalent reduced integer ratio has a denominator factor that is not 1, 2, or 5.

The denominator factors of 3/16 are all '2', so the decimal expansion terminates. The denominator factor of 4 2/11 = 46/11 is not a power of 2 or 5, so its expansion repeats. (It has a 2-digit repeat: 4.181818....)

__

All irrational numbers have decimal expansions that neither terminate nor repeat. Roots of numbers that are not perfect powers are one kind of number that falls into this category. For example, √5 is irrational, so its decimal expansion does not terminate or repeat.

Otras preguntas