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. In decimal form, this would be 1.4.
2) A decimal for 1/3 is called a repeating decimal because when 1 is divided by 3, the quotient does not terminate or end, but instead repeats the same pattern of digits indefinitely. In decimal form, it would be 0.3333....
3) To predict the decimal for 5/9, we can divide 5 by 9. The quotient is 0.555..., which means that the decimal representation of 5/9 is a repeating decimal. When we divide 5 by 9, we get a remainder of 5, so the decimal representation continues indefinitely with the digit 5 repeating.
4) The fraction that represents the shots that resulted in the basket is 9/27. To find the decimal, we divide 9 by 27. The quotient is 0.333..., which means that Jackson made 1/3 of his shots.
5) Terminating decimals are decimals that have a finite number of digits after the decimal point. For example, 0.25 is a terminating decimal. Repeating decimals, on the other hand, have a repeating pattern of digits after the decimal point. For example, 0.333... is a repeating decimal.
The end behavior of a decimal can give information about whether it represents a rational number or an irrational number. If a decimal terminates or has a repeating pattern, it represents a rational number. If a decimal does not terminate or have a repeating pattern, it is an irrational number.