Question 3: A smartphone has 64 GiB of internal storage. (a) Write an expression to calculate how many kilobytes (KiB) are in 64 GiB. (b) If each audio book takes 256 MiB, how many audio books can be saved on the phone (assuming the entire space is used)?
Answer (1)
To solve this problem, we need to perform unit conversions involving digital storage.
(a) Expression to Convert 64 GiB to KiB :
The goal is to convert the given storage from Gibibytes (GiB) to Kibibytes (KiB). Here's how it's done:
1 GiB is equal to 2 30 bytes, and 1 KiB is equal to 2 10 bytes.
Therefore, to find out how many KiB are in 1 GiB, we use:
1 GiB = 2 10 2 30 KiB = 2 20 KiB
So, for 64 GiB:
64 GiB = 64 × 2 20 KiB = 64 × 1 , 048 , 576 KiB = 67 , 108 , 864 KiB
Therefore, there are 67,108,864 KiB in 64 GiB.
(b) Number of Audio Books :
Each audio book takes 256 MiB. Let's convert this to bytes and compare it to the total space.
1 MiB is 2 20 bytes. So, 256 MiB is:
256 MiB = 256 × 2 20 bytes = 256 × 1 , 048 , 576 bytes = 268 , 435 , 456 bytes
Now, let's convert the total space in the phone from GiB to bytes:
64 GiB = 64 × 2 30 bytes = 64 × 1 , 073 , 741 , 824 bytes = 68 , 719 , 476 , 736 bytes
To find out how many audio books can be stored, divide the total space by the size of one audio book:
268 , 435 , 456 bytes/audio book 68 , 719 , 476 , 736 bytes ≈ 256 audio books
Therefore, the smartphone can store approximately 256 audio books.
