## Sig Figs in Scientific Notation

Matthew Chan 1B
Posts: 111
Joined: Sat Sep 07, 2019 12:16 am

### Sig Figs in Scientific Notation

Hi everyone, I just have a simple question regarding the number of significant figures/decimal places that we should include when we are writing in scientific notation. For example, (this is just some arbitrary value that I randomly thought of in my head) if I had the number 0.0011234, and I wanted to write it in scientific notation, how many sig figs would I include in the scientific notation? Would it be 1.12 x 10^-3 or would it be 1.1234 x 10^-3 or would it be something else? I guess what I'm asking is how does one know when to stop writing sig figs? Thanks!

Diana_Diep2I
Posts: 130
Joined: Sat Aug 17, 2019 12:17 am

### Re: Sig Figs in Scientific Notation

Hi! To answer your question, the number of sig figs in your scientifically notated number would depend on the given numbers in your equations. If the least number of sig figs in the problem is 3 digits, then yes you would write 1.12x10^-3. If the least number of sig figs in the problem is 5, then it would be 1.1234x10^-3. So basically, it would depend on the given numbers in your calculations that would determine the sig figs in your result.

WesleyWu_1C
Posts: 117
Joined: Thu Jul 25, 2019 12:16 am

### Re: Sig Figs in Scientific Notation

Yeah, to add on, scientific notation is just a way to show how many sig figs there are. For example, the number of sig figs in the value 100. is the same as 1.00 x 10^2, but you might miss the purposeful decimal point after 100 which indicates three sig figs. What determine the sig figs for any answer is the operation (addition, subtraction, division, or multiplication) that is being used.

Posts: 87
Joined: Sat Aug 24, 2019 12:15 am

### Re: Sig Figs in Scientific Notation

Basing off the other two replies I want to add on that like they stated, the correct amount of sig figs will mostly depend on what is in the rest of the problem (previous sig figs, addition/subtraction, or multiplication/division)

To expand in a situation where we are for example trying to reduce 120,050 into sig fig notation to for example,2, sig figs, we would proceed to make it 1.2 x 10^5. For sig figs, generally you would follow standard rounding rules except that for when the value would lands on 5, this goes down or up to the nearest even number: 1.25 would be rounded to 1.2, while 1.35 would be rounded to 1.4.

In addition, for addition/subtraction we use the sig fig rule and proceed to follow with the value that has the least amount of decimal spots in the problem. For example:

1.23455678 + 1.1= 2.3455678 (originally) but with sig figs it would simply be 2.3 as per 1.1 only have one decimal spot.

Lastly, for multiplication or division, we round to the amount of sig figs that was the lowest value in the problem of. For example:
1.1 X 1.00000= 1.1 because we go to 1.1 having only two sig figs as 1.00000 has six sig figs. or
2.50 x 3.555 = 8.8875 but with sig figs is 8.89. This is because we round to the three sig figs as present in 2.50.

This is mostly a more expanded version of the other two replies before me, but still hope this helps!

Robert Tran 1B
Posts: 118
Joined: Thu Jul 11, 2019 12:15 am

### Re: Sig Figs in Scientific Notation

The amount of sig figs that are used in the answer are determined by the lowest amount of sig figs in the raw data used in the calculations. Because of this, the amount of sig figs we use in scientific notation is determined by the accuracy of the raw data. When we use scientific notation the amount of sig figs is the same as the amount of digits in the first value (e.g. 1.297 in 1.297 x 10^-3 has 4 digits, so it has 4 sig figs). In the previous example value, if the least accurate raw data value had 2 sig figs, the value would be rounded to 1.3 x 10^-3.

Leila_4G
Posts: 114
Joined: Sat Sep 14, 2019 12:17 am

### Re: Sig Figs in Scientific Notation

When it comes to tests in class, how crucial is our accuracy of sig figs? Will we get the whole problem wrong if we have the wrong number of sig figs?