Question

worksheet iii
0.0075 gm = 7.5 km 0.00001 tl = 410 ml
0.00046 k8 = 46 ca 244,475.3 μs = 0.002444753 s
4,096 mb = 4.096 gb 210 hm = 2100000 cm
0.0002 μg = mg 448.5 cg = 4.485 g
0.00034 μl = cl 2,103.55 s = 2.10355 kg
11,120.33 ng = 0.001112033 cg 0.0000012 gl = 120000 cl
word problems

1. the distance from your home to the airport is 0.0000075 gm. how far is this in km?
2. there are 10 computers in the computer lab that each have 20 gb hard drives. how many bytes (b) of disk space do we have in the computer lab in total.
3. a challenge: convert 100125368477004 ng to teragrams.

adapted from http://www.morqwqalpcm.ca/curriculum_home.htm

Explanation:

Step1: Unit conversion factor for Gm to km

We know that \(1\space Gm = 10^{6}\space km\).

Step2: Perform the conversion

For \(0.0000075\space Gm\), we multiply by the conversion factor: \(0.0000075\times10^{6}\space km\).
Using the rule of exponents \(a\times10^{n}\), where \(a = 7.5\times10^{- 6}\) and \(n = 6\), \(7.5\times10^{-6}\times10^{6}=7.5\space km\).

Step3: Unit conversion factor for GB to B

We know that \(1\space GB=2^{30}\space B\approx10^{9}\space B\).
Each computer has \(20\space GB\), so for one computer, the disk - space in bytes is \(20\times10^{9}\space B\).
There are \(10\) computers, so the total disk - space is \(10\times20\times10^{9}\space B = 2\times10^{11}\space B\).

Step4: Unit conversion factor for ng to Tg

We know that \(1\space ng = 10^{-9}\space g\) and \(1\space Tg=10^{12}\space g\).
First, convert \(100125368477004\space ng\) to grams: \(100125368477004\times10^{-9}\space g=100125368.477004\space g\).
Then convert grams to teragrams: \(100125368.477004\div10^{12}\space Tg = 1.00125368477004\times10^{-4}\space Tg\)

Answer:

1. \(7.5\space km\)
2. \(2\times 10^{11}\space B\)
3. \(1.00125368477004\times 10^{-4}\space Tg\)