Isaac knows that ¼ is written as 0.25 in decimal form. How can he find a decimal for 7/5?
Explain why a decimal for ⅓ is called a repeating decimal.
Predict the decimal for 5/9. Divide to check your prediction, and describe the results.
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.
What is the difference between terminating and repeating decimals? How does the end behavior of a decimal relate to rational number or irrational number?
To find a decimal for 7/5, Isaac can perform long division by dividing 7 by 5. The quotient will be the decimal representation of 7/5.
A decimal for 1/3 is called a repeating decimal because when you divide 1 by 3, it results in 0.33333... The threes repeat infinitely, making it a repeating decimal.
Predicted decimal for 5/9 is 0.5555.... To check this prediction, divide 5 by 9. The result is indeed 0.5555... with the fives repeating.
The difference between terminating and repeating decimals is that terminating decimals have a finite number of digits after the decimal point, while repeating decimals have a pattern that repeats indefinitely. The end behavior of a decimal can help identify whether it is a rational number (if it terminates or repeats) or an irrational number (if it neither terminates nor repeats).
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.
To find the decimal representation of Jackson's shooting percentage, we divide the number of successful shots (9) by the total number of shots (27):
9 ÷ 27 = 0.3333...
Therefore, Jackson's shooting percentage from the free-throw line is 0.3333... or approximately 0.33 when rounded.