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**Oculus8596****Banned**- From: Great Lakes,Illinois
- Registered: 2024-09-18
- Posts: 126

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?

The best things in life are not always free.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,583

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

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

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**Oculus8596****Banned**- From: Great Lakes,Illinois
- Registered: 2024-09-18
- Posts: 126

Bob wrote:

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.

The best things in life are not always free.

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