1 Isaac knows that ¼ is written as 0.25 in decimal form. How can he find a decimal for 7/5?
2 Predict the decimal for 5/9. Divide to check your prediction, and describe the results.
3 What is the difference between terminating and repeating decimals? How does the end behavior of a decimal relate to rational number or irrational number?
Explain why a decimal for ⅓ is called a repeating decimal.
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.
1 To find a decimal for 7/5, Isaac can simply divide 7 by 5.
7 ÷ 5 = 1.4
Therefore, 7/5 is equal to 1.4 in decimal form.
2 Predicted decimal for 5/9 is 0.5555... (repeating).
However, dividing 5 by 9 gives:
5 ÷ 9 = 0.5555...
Therefore, the predicted decimal for 5/9 matches the actual result.
3 Terminating decimals are decimals that end, while repeating decimals are decimals that have a repeating pattern of digits. The nature of the decimal representation of a number can tell us whether the number is rational or irrational. A terminating decimal represents a rational number, while a repeating decimal represents a rational number as well.
For example, 1/3 can be represented as 0.3333... which is a repeating decimal. This is because when you divide 1 by 3, the result is 0.3333... which repeats infinitely.
4 The decimal form of Jackson's shot that resulted in the basket is:
9 ÷ 27 = 0.3333...
Therefore, Jackson made the basket 1 out of 3 times, which is equal to 0.3333... in decimal form.