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Oculus8596

Banned

From: Great Lakes,Illinois

Registered: 2024-09-18

Posts: 126

Convert to Scientific Notation

Convert each number to scientific notation.

A. 32.14

B. 0.0514

Question A

Count left from the decimal point until reaching a number that I will call x, where x lies between 1 and 10.

Doing this, 32.14 becomes 3.214. I now multiply 3.214 by 10 raised to the first power to get a final answer of
3.214 x 10^1.

Why does moving a decimal point to the left creates a positive exponent?

Question B

Count right from the decimal point until reaching a number that I will x, where x lies between 1 and 10.

Doing this, 0.0514 becomes 5.14. I now multiply 5.14 by 10 raised to the negative 2 power to get a final answer of 5.14 x 10^(-2).

Why does moving a decimal point to the right creates a negative exponent?

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,597

Re: Convert to Scientific Notation

This is why it works:

Positive powers of ten are 10, 100, 1000, etc so make a number bigger.

So if you reduce the value of the numeric part (32.14 becomes 3.214) you need to restore the value with a positive power of ten.

Negative powers of ten are fractional so they make a number smaller.

So if you increase the value of the numeric part (0.0514 becomes 5.14) you need to restore the value with a negative power of ten.

The number of places you have moved the decimal point tells you what power you need.

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

Oculus8596

Banned

From: Great Lakes,Illinois

Registered: 2024-09-18

Posts: 126

Re: Convert to Scientific Notation

This is why it works:

Positive powers of ten are 10, 100, 1000, etc so make a number bigger.

So if you reduce the value of the numeric part (32.14 becomes 3.214) you need to restore the value with a positive power of ten.

Negative powers of ten are fractional so they make a number smaller.

So if you increase the value of the numeric part (0.0514 becomes 5.14) you need to restore the value with a negative power of ten.

The number of places you have moved the decimal point tells you what power you need.

Bob

This is interesting. I did not know this fact.

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The best things in life are not always free.