scientifc notation 2

Question

The average person blinks approximately 15,000 times in a 16 hour day.  Kelly decides the average person will blink about 300 million times in a lifetime, is this reasonable? Mathematically justify your response with scientific notation

Answer 1

Scientific notation makes it easier for us to estimate quantities because we don't get lost in all those zeros.

 

Step 1:

15,000 becomes 1.5 x 1,000

which is the same as 1.5 x 10^4

1.5 x 10^4 blinks per day

 

Step 2:

Kelly thinks that translates to 300,000,000 blinks per lifetime.

3 x 100,000,000, count those zeros to get the scientific notation:

3 x 10^8 blink per lifetime

 

Step 3:

Now compare the information from Step 1 to the information from Step 2:

 

1.5 x 10^4 blinks/day  x _____ days/lifetime = 3 x 10^8 blink/lifetime

 

We need days/lifetime to figure this out.

According to the CDC, the average life expectancy from 2011 was about 79 years (source: http://www.cdc.gov/nchs/data/nvsr/nvsr61/nvsr61_06.pdf)

 

79 years/lifetime x 365 days/year = 28,835 days/lifetime

Let's round this and use scientific notation:

3 x 10^4

 

Step 4:

1.5 x 10^4 blinks/day  x 3 x 10^4 days/lifetime = 4.5 x 10^8 blink/lifetime

 

So compared to Kelly's 3 x 10^8 blinks/lifetime falls a bit short, but it is one the same order of magnitude as the answer we calculated (4.5 x 10^8 blink/lifetime, note the 10^8 in both answers).

 

Answer:

So we say Kelly's answer was reasonable, because the two answers are on the same order of magnitude as our answer using the CDC 2011 data.

 

 

 

Hope this helps!

Answer 2

15000 blinks/day *365 days/year *72 years/lifetime =almost 400,000,000 times or 400 million