## Powers of 10

Elyssa Smith 4B
Posts: 58
Joined: Wed Sep 18, 2019 12:22 am

### Powers of 10

Can someone explain when we know to write answers in powers of 10 and when it's not necessary?

Deepika Reddy 1A
Posts: 125
Joined: Thu Jul 11, 2019 12:15 am

### Re: Powers of 10

It depends on the answer you get. if there are a lot of decimal places or zeros after the answer, then it should be in scientific notation. When you use a calculator, it'll put the number in scientific notation if it's a really big or small number.

Sofia Q
Posts: 49
Joined: Sat Aug 17, 2019 12:15 am

### Re: Powers of 10

Calculations should be done in the power of 10 to avoid any misunderstandings. For example, if in a problem regarding molarity, the formula calls for the number of moles over liters, however, if you were to be given mL and not convert it before inserting, without future modification your calculated concentration would be wrong.

Naren_Ramesh_4F
Posts: 105
Joined: Sat Aug 17, 2019 12:18 am

### Re: Powers of 10

Powers of 10 in an answer should be utilized when you have an extremely large or small numerical answer. I don't believe there is necessarily a penalty for not using powers of 10 in general except that it may cause confusion. The most important thing I think is that your units are accurate for what you calculated for.

Doreen Liu 4D
Posts: 54
Joined: Wed Sep 11, 2019 12:17 am

### Re: Powers of 10

You can write an answer in powers of 10 when it can be easily understood and for sig figs purposes.

805422680
Posts: 103
Joined: Sat Sep 14, 2019 12:16 am

### Re: Powers of 10

Using powers of ten is really up to your discretion. If you have 104859 grams, you may want to change that into kilograms (104.859 kg). If you have a really small number of grams, for example, .00456 grams, you would probably want to convert that to 4.56 mg.

Sanjana K - 2F
Posts: 102
Joined: Sat Sep 07, 2019 12:17 am
Been upvoted: 1 time

### Re: Powers of 10

When performing calculations, you generally want to keep the powers (especially if you're dealing with a very small or large number). After calculations, you could express the powers in simpler units (just for convenience or when in a lab setting, where you can't measure negative exponents of 10). So for example, if your answer is 2x10^(-3) L, you can express this as 2mL instead.

Kaitlyn Jang 1F
Posts: 45
Joined: Sat Aug 17, 2019 12:16 am

### Re: Powers of 10

Can someone explain when we know to write answers in powers of 10 and when it's not necessary?

Scientific notation is most typically used when the number of zeros in a number is too long to write out (usually starting around 3 or 4 decimal zeros before or after the first non-zero number). For example, 0.0004 would be better written as 4x10^-4 and 45,000,000 would be better written as 4.5x10^7.

Manav Govil 1B
Posts: 104
Joined: Sat Sep 07, 2019 12:19 am

### Re: Powers of 10

An important note: powers of ten are not counted in sig-figs!!!!!

Both 0.000025 and 2.5 * 10^-5 have 2 sig-figs.

Powers of 10 are really just used for convenience in a calculation. For example, instead of dividing 1.03 moles by 45 mL to find the molarity, it is better to divide 1.03 moles by 45 * 10^-3 L (or 4.5 * 10^-4 L) to get 23. M.

Subashni Rajiv 1K
Posts: 101
Joined: Wed Sep 18, 2019 12:16 am

### Re: Powers of 10

You generally use sig figs when dealing with number with 2 or more powers of 10.

Michelle N - 2C
Posts: 117
Joined: Wed Sep 18, 2019 12:19 am

### Re: Powers of 10

I believe that using scientific notation just makes it easier, especially when (like what everyone said above) the numbers become too small or too large. I think it also comes into play when there's a LOT of zeros involved, just to simplify. Lastly, I think using the powers of 10 also helps when it comes to converting units (e.g. ml to l, etc).