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sologuitar

Member

Registered: 2022-09-19

Posts: 467

Number to Scientific Notation

College Algebra
Section R.2

Write each number in scientific notation.

A. 9582

Answer: 9.582 x 10^(3)

To obtain the answer, I moved the decimal point 3 places to the left.
This yielded 9.582. Why is 10 raised to a positive power?

B. 0.285

Answer: 2.85 x 10^(-1)

To obtain the answer, I moved the decimal point one place to the right.
This yielded 2.85. Why is 10 raised to a negative power?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,198

Re: Number to Scientific Notation

When you change a number into scientific notation the actual value of the number must stay the same.  The rule is to insert a decimal point between digits one and two and then correct the value by multiplying by a power of ten.

9582 = 9.582 x 1000 so the correct power is 3  (1000 = 10^3)

0.285 = 2.85 x 1/10 so the correct power is -1       1/10 = 10^(-1)

Back in the days when logs were used to do calculations it was an essential part of the process so that the table book only needed to have logs of numbers between 1 and 10.

Now with calculators it allows entry and display of numbers which would otherwise exceed the available display size.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Number to Scientific Notation

Calculators do it all today but calculators also hinder the learning process to some degree. Do you agree?

Scientific notation helps scientists to read and write big and small numbers in a unique, to the point way.

Yes? No?

P. S. We will stick to one topic at a time. It does make sense for me to post many questions representing various math topics.