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

##### 3 Answers
Jun 21, 2016

2555

Jun 21, 2016

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.

$2600$ km

#### Explanation:

If the figures $2222$ km and $333$ km were totally accurate, then the sum would be:

$2222 + 333 = 2555$ km

However, since the question speaks of significant digits, the implication is that the figures $2222$ km and $333$ km are only quoted to the nearest km. One notation used to specify this possible range of error in the figures would be:

$2222 \pm 0.5$ km and $333 \pm 0.5$ km

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

$2555 \pm 1$ km

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

$\left[2554 , 2556\right)$ km

Note that rounded to the nearest $10$ km, the ends of this interval are $2550$ and $2560$. So we cannot specify a single figure with $3$ significant digits.

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 $100$ km and having $2$ significant digits:

$2600$ km

Jun 22, 2016

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.