Question

How do you add 32 500 + 26 823 - 56000 *to the correct number of significant digits*?

Answer 1

To the correct number of significant digits, the answer is 3000.

Explanation:

Important significant figure rules for this problem

1. Non-zero digits are always significant.
2. If there is no decimal point, trailing zeros are not significant.
3. The last significant figure is considered an uncertain digit.
4. When a trailing zero or an uncertain digit is added to or subtracted from another digit, the result is an uncertain digit.

When adding and subtracting,

1. Add or subtract as usual.
2. Round off the answer to include only 1 uncertain digit.

The answer to your problem

Step 1. Add and subtract as usual

`color(white)(m)32color(white)(l)color(red)(5)00`
`+26color(white)(l)82color(red)(3)`
`-5color(red)(6)color(white)(l)000`
`stackrel(————)(color(white)(mll)color(red)(3)color(white)(l)color(red)(323))`

I have marked the uncertain digits in `color(red)("red")`.

Step 2. Round off the answer to include only 1 uncertain digit.

The rounded answer is `color(red)(3)color(white)(l)000`.

The rounded answer contains one uncertain digit, and the trailing zeroes serve only as placeholders for locating the decimal point.

Therefore, you can say that your number has `1color(white)(l) bb("significant digit")`.

`color(red)(3)color(white)(l)000 → { (color(red)(1)color(white)(l) "uncertain digit, significant " color(white)(mm)color(green)(sqrt())), (3color(white)(l)"trailing zeroes, not significant "color(red)(×)):}`