Scientific Notation

[Holly-Kay]

Hey Guys, i need some help with scientific notation. I just don't quite grasp the concept...
I have a sample question here i don't understand:

"What is 1 560 200 km written in scientific notation correct to two significant figures?"

Thank you so much!

[RuiAce]

The first significant figure is the first number on the left that's not a 0. In our case, that is basically the 1.

We want our answer to 2 s.f.
Therefore our digit of interest is the third number on the left.

This number is 6. Because 6 is a number greater than or equal to 5, we must round up. The digit that will be rounded up will be, of course, the second digit.

Hence we round up the 5. 5 rounds up to a 6, so we will have \(1.6 \times 10^{something}\)

As for the something, we count how many 'jumps' we need to get from the right to between 1 and 5. For indication, the jumps will be represented by commas:
1,5,6,0,2,0,0

There are 6 jumps, so that something will be a 6.

Hence the answer is \(1.6\times 10^6\)

[jakesilove]

Hey Guys, i need some help with scientific notation. I just don't quite grasp the concept...
I have a sample question here i don't understand:

"What is 1 560 200 km written in scientific notation correct to two significant figures?"

Thank you so much!

Hey! So, there are a few concepts that need to be understood to answer this question.

Significant figures

Significant figures is a measure of how many numbers in your answer are important. To calculate significant figures, you go to the first 'important' (think non-zero, although this isn't always the case), and count from there. In this case, the first significant figure in 1 560 200 km is the first number; 1. If they had given you 01560200 km, the first significant figure would still be one, because the zero plays no role and thus is not significant!

Two significant figures, therefore, is the first 'two' digits starting from the number 1. Thus, our two sig fig value is 1,600,00 km. Note that I have rounded the second value UP, because the THIRD value was greater than or equal to 5.

Scientific notation

To write a value in scientific notation, it HAS to be in the form



Where # is any number, and x is any integer. For instance,



is scientific notation for 120. Remember, every time you multiply by 10, you just add a zero to the answer. This, however, is not in scientific notation



Note that this 'value' is exactly the same as above (120), but ISN'T in scientific notation as it must be #.# (ie. the unit value, then a decimal value).

In this case, our unit/decimal value must be 1.6 (as our answer is 1,600,000 km). What do we multiple by?



Well, we add a zero every time we multiple by ten.



etc. etc. Count how many times the decimal place is moved, and you'll get



Edit. As always, Rui beat me to it. Posting anyway

[Holly-Kay]

THANK YOU