This problem should help you see the need for scientific notation of numbers and

Question

This problem should help you see the need for scientific notation of numbers and give you a feeling for the large and small scales of the universe. Estimate your answers but feel free to check your numbers with a calculator.

Grains of sand are very small - about 2500 grains fit in one cubic centimeter (cm3) of sand. A cm3 is a small cube measuring one cm on each side and is about the size of your little finger tip. Given that there are one million cubic centimeters (cm3) in one cubic meter (m3), how many grains are there in 1 m3 of sand?

If you counted one grain of sand each second, how many seconds would it take you to count all the grains in one cubic meter?

We want to change this to years: how many seconds are there in one year?

Using the previous 2 answers, calculate how many years would it take to count all the grains of sand in one cubic meter?

One can estimate the total length of coastlines along all the beaches in the world using a globe, a piece of string, and a ruler. Roughly, there are 200,000 km of beaches in the world. How many meters is this?

We now want to calculate the total volume of sand on all the world's beaches. Use the length of beach from the previous question, say that the average width of a beach is 20 meters, and that the average depth of sand is 2 meters. What is the total volume of sand, in m3, of all the world's beaches?

Estimate how many grains of sand there are on all the beaches of the world.

There are something like 100 billion (1011) stars in a typical galaxy, and there are about 100 billion galaxies in the universe. How many stars are there in the universe?

Now we consider the very small. Each of us is made of a very large number of atoms, each atom being only about 1/100,000,000 cm (10-8 cm) in diameter. There are about 1023 atoms in a cubic centimeter, and about 1028 atoms in our bodies. How does this compare with the number of stars in the universe (i.e. how many times more atoms are there in your body than stars in the universe)?

A typical star, such as the Sun, has about 1029 times as many atoms as your body. How many atoms are there in a star?

Now let's go for the big one.... How many atoms are there in all the stars of the universe?

Explanation / Answer

answer 1- scientific notation deals with the number. it is the way of writing number. students finds there is alot of problems in writing in large number like writing the distance between sun and earth and other planet. it reaches upto billion to trillion in number. there are so many zeros in writing these numbers and also finds problem in writing small numbers like measuring weight of radius of molecule and atoms and also the weight of atoms. they are very small reach to micron, nanometer, angustrum, picometer, fermi etc.

scientific notation is the smart way to writing the whole large number to small decimal number.

answer 2- number of sand grain is 1 cm3 box. is 2500

so 1 cm3 = 0.000001m3

so in 1 m3= 2500*1000= 2500000 or 2.5* 106 sand grain

answer 3- if I count one sand grain in 1 second then the time i will take to calculate 2500000 sand grain will be

2500000 second or 41666.66 minute or 694.4 hourse 28.9 days

answer4- how many seconds in year

1 min = 60 sec

1 hours = 60*60 = 3600 sec

1 day= 24* 3600= 86400 sec

I year = 365 days = 365* 86400= 31536000= 3.15*107 seconds

answer 12- there are approximately 1078 to 1080 atoms in present in all star of the universe

answer - 11 - atoms in human body depends upon its weight letc a person weight is 60kg then atoms present in 6* 10 27

according to question sun is consist atoms of 1029 times than atoms a human body consist

so the number of atoms in the sun will be 1029* 6*1027 = 6174*1027 = 6.174* 1030

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