Question

Write each rational number in decimal form. Then tell whether the decimal is a terminating or repeating decimal.

1.) -11/16
2.) 5/33
3.) 8/9

Answer 1

To find the decimal form of a fraction, divide the numerator by the denominator. The decimals -0.6875, 0.1515..., and 0.8888... result from the fractions -11/16, 5/33, and 8/9, respectively. The first is terminating while the latter two are repeating decimals.

Step-by-step explanation:

The question asks to convert rational numbers into decimal form and determine if the decimal is terminating or repeating.

1. -11/16: To convert this fraction, simply divide -11 by 16, which equals -0.6875. This is a terminating decimal because the division ends with a finite number of digits.
2. 5/33: Dividing 5 by 33 gives approximately 0.1515. Observing the pattern, you'll notice that '15' repeats, hence 5/33 is a repeating decimal and can be written as 0.1515...
3. 8/9: Similarly, dividing 8 by 9 yields approximately 0.8888..., which is clearly repeating. This decimal repeats the single digit '8', thus making it a repeating decimal.

All three cases involve simple division and recognizing patterns in the resulting decimals. Remember, a terminating decimal is one that ends after a certain number of digits while a repeating decimal has one or several digits that repeat infinitely.