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Significant Digits: Additional Details (page 3 of 3)

Sections: General rounding, Rounding and significant digits

How do you round when they give you a bunch of numbers to add? You would add (or subtract) the numbers as usual, but then you would round the answer to the same decimal place as the least-accurate number. For instance:

• Round to the appropriate number of significant digits:

13.214 + 234.6 + 7.0350 + 6.38

Looking at the numbers, I see that the second number, 234.6, is only accurate to the tenths place, so the answer will have to be rounded to the tenths place:

13.214 + 234.6 + 7.0350 + 6.38 = 261.2290

Rounding to the tenths place, I get: Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

13.214 + 234.6 + 7.0350 + 6.38 = 261.2

Here's another example:

• Round 1247 + 134.5 + 450 + 78 to the appropriate number of significant digits.

Looking at each number, I see that I will have to round the final answer to the nearest tens place, because 450 is only accurate to the tens place. That is:

1247 + 134.5 + 450 + 78 = 1909.5

...but I will round this to the tens place:

1247 + 134.5 + 450 + 78 = 1910

How do you round, when they give you numbers to multiply (or divide)? You would multiply (or divide) the numbers as usual, but then you would round the answer to the same number of significant digits as the least-accurate number. For instance, if they give you something like:

• Simplify, and round to the appropriate number of significant digits:

16.235 × 0.217 × 5

First, I would note that 5 has only one significant digit, so I will have to round my final answer to one significant digit.  The product is:

16.235 × 0.217 × 5 = 17.614975

...but since I can only claim one accurate significant digit, I will need to round 17.614975 to 20, which is accurate to one significant digit.

16.235 × 0.217 × 5 = 20

Here's another example: 

• Find the product of 0.00435 and 4.6 to the appropriate number of digits.

First I will multiply:

0.00435 × 4.6 = 0.02001

Looking at the original numbers, 4.6 has only two significant digits, so I will have to round 0.02001 to two significant digits. In other words, I would report the answer as being 0.020.

0.00435 × 4.6 = 0.020

Don't try to say that the answer should be 0.02, because this is only one significant digit (the "2"). The trailing zero indicates that "this is accurate to the thousandths place", and is therefore a necessary part of the answer.

Just remember the difference:

For adding, use "least accurate place".

For multiplying, use "least significant digits".

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