# What is the sum of 2222 km and 333 km using the correct number of significant digits?

##### 3 Answers

2555

Note: I have based this answer on analysis of error ranges based on the significant figures we are given. This may be different from the rules you are taught concerning significant digits.

#### Explanation:

If the figures

#2222+333 = 2555# km

However, since the question speaks of significant digits, the implication is that the figures

#2222+-0.5# km and#333+-0.5# km

Using this notation, the sum with error range would be:

#2555+-1# km

The precise measurement of the sum could be anywhere in the half open interval:

#[2554, 2556)# km

Note that rounded to the nearest

If we want to specify one number approximating the sum, which is correct to its implicit number of significant digits, then we are stuck with rounding to the nearest

#2600# km

2222 km + 333 km = 2555 km

#### Explanation:

When taking measurements, the last digit is always an estimate. When adding or subtracting measurements, the result can be no more precise than the measurement with the fewest decimal places.

https://engineering.purdue.edu/~asm215/topics/calcrule.html

http://tournas.rice.edu/website/documents/SignificantFigureRules1.pdf

http://www.quickanddirtytips.com/education/math/how-to-calculate-with-significant-figures

2222 km and 333 km are both whole numbers with no decimal places, and are both precise to the nearest 1 km. Their sum should be reported as 2555 km.