1.) Isaac knows that ¼ is written as 0.25 in decimal form. How can he find a decimal for 7/5?
2.) Explain why a decimal for ⅓ is called a repeating decimal.
3.) Predict the decimal for 5/9. Divide to check your prediction, and describe the results.
4.) Jackson is practicing basketball. He makes a basket from the free-throw line 9 out of 27 shots. Write the decimal from the fraction of Jackson’s shot that resulted in the basket.
5.) What is the difference between terminating and repeating decimals? How does the end behavior of a decimal relate to rational number or irrational number?
1.) To find a decimal for 7/5, Isaac can divide 7 by 5 using long division. The decimal form of 7/5 is 1.4.
2.) A decimal for ⅓ is called a repeating decimal because when you divide 1 by 3, the division does not end and keeps repeating the same sequence of digits, which is 0.3333... The ellipsis (...) indicates that the sequence of 3's continues indefinitely.
3.) To predict the decimal for 5/9, we can divide 5 by 9 using long division. The decimal form of 5/9 is 0.5555... The division indicates that the digit 5 will repeat indefinitely.
4.) Jackson made 9 out of 27 shots, so the fraction of his shots resulting in a basket is 9/27. To write this as a decimal, we divide 9 by 27. The decimal form is 0.3333..., which means he made roughly 33.33% of his shots.
5.) Terminating decimals have a finite number of decimal places and end, whereas repeating decimals have repeating patterns of digits that continue indefinitely. The end behavior of a decimal can indicate whether it is a rational number or an irrational number. Rational numbers can be expressed as either terminating or repeating decimals, while irrational numbers cannot be expressed as either and have an infinite, non-repeating decimal representation.