How many significant digits are contained in the number 1804.00?

1 Answer
Jul 30, 2016

Answer:

#6#

Explanation:

The first thing to notice here is that your number contains three non-zero digits, #1#, #8#, and #4#. As you know, all non-zero digits are significant.

#color(blue)(18)0color(blue)(4).00 -># #3color(white)(a)color(blue)("non-zero digits")#

Next, notice that your number contains a sandwiched zero, which is a zero digit that follows and is followed by a non-zero digit. Sandwiched zeros are significant.

In your case, you have a zero that is sandwiched between #8# and #4#, both non-zero digits.

#color(blue)(18)color(red)(0)color(blue)(4).00 -> {(3color(white)(a)color(blue)("non-zero digits")), (1color(white)(a)color(red)("sandwiched zero")) :}#

Finally, notice that your number also contains two trailing zeros. A trailing zero is zero that follows a decimal point or a non-zero digit and is not followed by a non-zero digit.

Trailing zeros that follow the decimal point are always significant.

In your case, you have

#color(blue)(18)color(red)(0)color(blue)(4).color(darkgreen)(00) -> {(3color(white)(a)color(blue)("non-zero digits")), (1color(white)(a)color(red)("sandwiched zero")), (2color(white)(a)color(darkgreen)("trailing zeros")) :}#

Therefore, your number has a total of

#1804.00 -> 6# significant figures.