Question

Interactive digital version available - link: https://access.openupresources.org/curricula/our6-8math/en/supporting-material/7569/index.html

After a while, Jada picks up a coin that seems different than the others. She notices that the next day, only half of the coin is left!
On the second day, only 1/4 of the coin is left.
On the third day, 1/8 of the coin remains.
What fraction of the coin remains after 6 days?




What fraction of the coin remains after 28 days? Write an expression to describe this without computing its value.


Does the coin disappear completely? If so, after how many days?

Answer 1

After 6 days 1/64 of the coin will remain, while after 28 days 1/268435456 will remain. Now, it will never completely disappear, since it can always be reduced to a larger number.

Explanation:

Since after a while, Jada picks up a coin that seems different than the others, and she notices that the next day, only half of the coin is left, while on the second day, only 1/4 of the coin is left and, on the third day, 1/8 of the coin remains, to determine what fraction of the coin remains after 6 days, what fraction of the coin remains after 28 days and determine if the coin will disappear completely, the following calculation must be performed:

1/2 ^ 6 = X

0.015625 = X

1/64 = X

1/2 ^ 28 = X

0.0000000037252902984619140625 = X

1/268435456 = X

Thus, after 6 days 1/64 of the coin will remain, while after 28 days 1/268435456 will remain. Now, it will never completely disappear, since it can always be reduced to a larger number.