# Round the following number to $4$ significant figures: $794834.$

Round the following number to $$4$$ significant figures:
$$X=794834.$$

For the number $$X=794834$$, I simply observed that all the digits in here are significant. The $$4^{th}$$ significant digit in this case, is $$8$$ and the $$5^{th}$$ digit is $$3$$. Now, as $$3 \lt 5$$ so, we can represent the given number as $$X \approx 7948 \times 10^2.$$ This is the scientific representation and $$7948 \times 10^2$$ has $$4$$ significant digit.

My question, is, if we were given a number like $$Y=794894,$$ then should I round it off as $$Y \approx 7949 \times 10^2.$$ In this scientific representation $$7949 \times 10^2$$ has $$4$$ significant digits. I also changed the $$4^{th}$$ significant digit in $$7949 \times 10^2$$ to $$9$$ as, the $$5^{th}$$ digit in $$794894$$ was $$9$$ and $$9 \gt 5.$$

I am much new in working with rounding off numbers upto some number of significant digits and hence, I am not sure whether I have understood the concept or not.

Till now, I am only used to rounding off numbers like $$Z=45.67$$ upto the $$3^{rd}$$ significant figures. So, this is my first time for rounding off a whole number.

Easiest way to think about this is to write $$X=794834$$ in the form $$X=7.94834\times10^5$$ & then make it $$4$$ significant figures to get $$X \approx 7.948\times10^5$$ , using your "known" way to handle fractional numbers.
With $$Y=794894$$ , we get $$Y=794894=7.94894\times10^5$$ , hence when we make it $$4$$ significant figures , we will get $$Y \approx 7.949\times10^5$$ , using your "known" way to handle fractional numbers.
It is a "standard" format to write using the numbers between $$1$$ & $$10$$ , where the Power of $$10$$ (Either Positive or Negative) will fix the Decimal Point.
• Indeed that's agreat way to think about it! Now, similarly if we wanna round off the number 630 in 4 sig fig then, the answer would be, $6.300\times 10^2$. Similarly, if it was given to round off 630 in 5 sig fig, then it would be, $6.3000\times 10^2$. Did I get this? Aug 16, 2023 at 15:03