Question

Part A

Theresa and her brother, Ruben, are getting phones that each have 32 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation.

Part B
Theresa’s parents, Cal and Julia, are getting phones that each have 64 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation.

Part C
Because they are getting four new phones, the family also gets two free tablets. Each tablet has 16 gigabytes of storage. How many bits of storage come with each tablet?

Part D
Theresa talked her parents into getting SD cards for her phone and her brother’s phone. Inserting an SD card into a phone gives it more storage. They both get 8-gigabyte SD cards. How many bits of storage come with each SD card? Type your answer in both scientific and standard notation.

Part E
With their plan, the family also gets access to storage on the cloud. They can store a total of 40 gigabytes on the cloud. How many bits of storage do they get on the cloud? Type your answer in both scientific and standard notation.

Answer 1

Part A)

scientific notation ------>
`2.56*10^(11)\ bits`

standard notation ----->
`256,000,000,000\ bits`

Part B)

scientific notation ------>
`5.12*10^(11)\ bits`

standard notation ----->
`512,000,000,000\ bits`

Part C)

scientific notation ------>
`1.28*10^(11)\ bits`

standard notation ----->
`128,000,000,000\ bits`

Part D)

scientific notation ------>
`6.4*10^(10)\ bits`

standard notation ----->
`64,000,000,000\ bits`

Part E)

scientific notation ------>
`3.2*10^(11)\ bits`

standard notation ----->
`320,000,000,000\ bits`

Explanation:

we know that

`1\ Gigabyte=1*10^(9)\ bytes\\ 1\ byte=8\ bits`

therefore

`1\ Gigabyte=8*10^(9)\ bits`

Part A

Theresa and her brother, Ruben, are getting phones that each have 32 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation

we know that

Each phone have 32 gigabytes of storage

so

using proportion

`(1)/(8*10^(9))(\ Gigabytes)/(\ bits) =(32)/(x)(\ Gigabytes)/(\ bits)\\ \\x=32*8*10^(9)\\ \\x=256*10^(9)\ bits\\ \\x=2.56*10^(11)\ bits`

scientific notation ------>
`2.56*10^(11)\ bits`

standard notation ----->
`256,000,000,000\ bits`

Part B

Theresa’s parents, Cal and Julia, are getting phones that each have 64 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation.

we know that

Each phone have 64 gigabytes of storage

so

using proportion

`(1)/(8*10^(9))(\ Gigabytes)/(\ bits) =(64)/(x)(\ Gigabytes)/(\ bits)\\ \\x=64*8*10^(9)\\ \\x=512*10^(9)\ bits\\ \\x=5.12*10^(11)\ bits`

scientific notation ------>
`5.12*10^(11)\ bits`

standard notation ----->
`512,000,000,000\ bits`

Part C

Because they are getting four new phones, the family also gets two free tablets. Each tablet has 16 gigabytes of storage. How many bits of storage come with each tablet?

we know that

Each tablet have 16 gigabytes of storage

so

using proportion

`(1)/(8*10^(9))(\ Gigabytes)/(\ bits) =(16)/(x)(\ Gigabytes)/(\ bits)\\ \\x=16*8*10^(9)\\ \\x=128*10^(9)\ bits\\ \\x=1.28*10^(11)\ bits`

scientific notation ------>
`1.28*10^(11)\ bits`

standard notation ----->
`128,000,000,000\ bits`

Part D

Theresa talked her parents into getting SD cards for her phone and her brother’s phone. Inserting an SD card into a phone gives it more storage. They both get 8-gigabyte SD cards. How many bits of storage come with each SD card? Type your answer in both scientific and standard notation

we know that

Each SD card have 8 gigabytes of storage

so

using proportion

`(1)/(8*10^(9))(\ Gigabytes)/(\ bits) =(8)/(x)(\ Gigabytes)/(\ bits)\\ \\x=8*8*10^(9)\\ \\x=64*10^(9)\ bits\\ \\x=6.4*10^(10)\ bits`

scientific notation ------>
`6.4*10^(10)\ bits`

standard notation ----->
`64,000,000,000\ bits`

Part E

With their plan, the family also gets access to storage on the cloud. They can store a total of 40 gigabytes on the cloud. How many bits of storage do they get on the cloud? Type your answer in both scientific and standard notation

we know that

The cloud have 40 gigabytes of storage

so

using proportion

`(1)/(8*10^(9))(\ Gigabytes)/(\ bits) =(40)/(x)(\ Gigabytes)/(\ bits)\\ \\x=40*8*10^(9)\\ \\x=320*10^(9)\ bits\\ \\x=3.2*10^(11)\ bits`

scientific notation ------>
`3.2*10^(11)\ bits`

standard notation ----->
`320,000,000,000\ bits`