Question

How many significant digits are contained in the number 1804.00?

Answer 1

`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.