# scientific notation help please

#### hmwin

##### New member
9.7 X 10^10
__________
9.74 X 10^7

I am assuming that you divide 9.7 by 9.74 and that answer would be times 10^3

so... 9.7/9.74 = .99589... X 10^3

so... 9.9 X 10^4 but...the answer needs to be rounded to the nearest whole number. The nearest whole number is 10, but the number is supposed to be between 1 and 9. Would 9 be the nearest whole number? or would it be 1 X 10^(3 or 5?)

There, I gave as much information as I could!

#### mmm4444bot

##### Super Moderator
Staff member
hmwin said:
9.7 X 10^10
__________
9.74 X 10^7

… the answer needs to be rounded to the nearest whole number …

Why do you need to round the answer? Do the instructions for this exercise tell you to round the final answer?

Your first calculation of 0.99589 x 10^3 is correct, but this expression is not scientific notation.

I think you realize that it's not scientific notation because you changed it to 9.9 x 10^4.

Your mistake is that you increased the exponent from 3 to 4.

We need to decrease the exponent from 3 to 2, instead.

0.99589 x 10^3 = 995.89

9.9589 x 10^2 = 995.89

9.9589 x 10^4 = 9958.9

Understand?

If you are supposed to round off 995.89 to the nearest whole number, then the final answer is 996.

If you are supposed to take into account significant digits, then the answer will be different.

If you want more help with this exercise, then please post all of the given instructions.

#### hmwin

##### New member
The directions say to round the answer to the nearest whole number. It doesn't say the answer has to be in scientific notation, so what you say should be correct. Thank you for your help!

I have one other question that has me stuck.

The speed of computers is measured in number of calculations per picosecond. There are 3.6 X 10^15 picoseconds per hour. What fraction of a second is a picosecond?

I know a ratio is involved, but I'm having a hard time figuring out the equation to get me started. I'm sure it has something to do with seconds per hour. Can you help me figure out where to begin?!

#### mmm4444bot

##### Super Moderator
Staff member
hmwin said:
… It doesn't say the answer has to be in scientific notation, so what you say should be correct. …

Our posts crossed in cyberspace; did you see my edit?

I added a comment about significant digits. Are you supposed to follow any guidelines for significant digits?

#### hmwin

##### New member
I believe 996 is correct also. I posted one other question for your help with! Sure appreciate it!

#### mmm4444bot

##### Super Moderator
Staff member
hmwin said:
… I'm sure it has something to do with seconds per hour.

Yup, yup.

Use the ratio of seconds-per-hour as a conversion factor to discover how many picoseconds are in one second.

Alternately, you could look up the SI prefix "pico" to discover the same thing without doing any calculation.

Once you know the number of picoseconds in one second, then the answer follows naturally.

EG:

There are one millon microseconds in one second, so one microsecond is one millionth of one second.

Let me know if you need help with set up and use of a conversion factor.

#### hmwin

##### New member
so...

3.6 X 10^15
__________
1 X 10^-12

is that correct so far?

#### mmm4444bot

##### Super Moderator
Staff member
hmwin said:
3.6 X 10^15
__________
1 X 10^-12

is that correct so far?

No.

Please explain your reasoning because I'm not sure what you're trying to do.

Where did you get 10^(-12)?

What do you think that it represents?

#### hmwin

##### New member
In wikipedia it says the SI for pico is to 10^-12.

#### mmm4444bot

##### Super Moderator
Staff member
hmwin said:
In wikipedia it says the SI for pico is to 10^-12.

Great!

Now tell me what you learned from that in terms of this exercise.

#### hmwin

##### New member
wellllll... 3.6 X10^15 is picoseconds per hour, is there some kind of subtraction of powers here? I all for hints here!

#### hmwin

##### New member
another thought....

3.6 X 10^15
__________
60 X 10 ^-12

3.6/60 = .6

.6 X 10^15-(-12) or .6 X 10^27 ???

#### mmm4444bot

##### Super Moderator
Staff member

You did not answer either of my two questions.

I cannot tell what you're thinking, so I do not understand what you're trying to accomplish with these divisions you're posting.

You need to determine how many picoseconds are in one second.

This can be done by using the given information along with a conversion factor.

OR, it can be done by reasoning from the SI prefix information.

Do not combine these two methods; use one OR use the other.

What are you trying to do?

#### hmwin

##### New member
a picosecond is 10^-12...

so if there are 60 seconds per one hour, there are 10^-12 picoseconds per second?! is that correct?

#### hmwin

##### New member
So....

what fraction of a second is a picosecond would be

1
____
10^12

correct?!

#### mmm4444bot

##### Super Moderator
Staff member
hmwin said:
a picosecond is 10^-12

This is not a complete statement.

A picosecond is 10^(-12) what?

(This type of partial statement is no different than if I were to tell you that \$10 is 10^(-1). It makes no sense.)

-
hmwin said:
… if there are 60 seconds per one hour …

Are you serious?

-
hmwin said:
… there are 10^-12 picoseconds per second?

No.

Do you understand the difference between the following two numbers?

10^12

10^(-12)

If you continue to ignore my direct questions to you, I will stop trying to help you.

Got the message?

#### mmm4444bot

##### Super Moderator
Staff member
hmwin said:
what fraction of a second is a picosecond would be

1
____
10^12

correct?

This is correct.

(From what you've posted in this thread, I have no idea how you arrived at this result. Perhaps, you finally realized how to interpret an SI prefix.)

Here's the other way -- using a conversion factor.

Given: 3.6 x 10^15 picoseconds in one hour.

Use the fact that one hour equals 3600 seconds to set up a conversion factor.

3600 = 3.6 x 10^3

In order to obtain the unit "picoseconds per hour", the conversion factor needs to have the units "hour" on top and "second" on bottom.

$$\displaystyle \frac{3.6 \times 10^{15} \; \text{picoseconds}}{1 \; \text{hour}} \cdot \frac{1 \; \text{hour}}{3.6 \times 10^3 \; \text{second}} \; = \; \frac{3.6 \times 10^{15} \; \text{picoseconds}}{3.6 \times 10^3 \; \text{second}}$$

The arithmetic works out to 10^12 picoseconds per second.

Since there are one billion picoseconds in one second, one picosecond is one-billionth of one second.

10^(-12) = one-billionth