Question

Question #a89be

Answer 1

`8`

Explanation:

For starters, you know that all non-zero digits are significant, so you can say that your number has at least `3` significant figures because it contains `3` non-zero digits.

`color(black)(color(red)(1)0color(red)(9)0.00color(red)(1)0) -> " 3 non-zero digits: " { color(red)(1), color(red)(9), color(red)(1) }`

Now, you should also know that all zeros that are sandwiched between two non-zero digits are significant. In other words, if a zero follows a non-zero digit and is followed by a non-zero digit, regardless if other zeros are adjacent, it is significant.

In your case, you have `4` sandwiched zeros. The first sandwiched zero follows `color(red)(1)` and is followed by `color(red)(9)`

`color(black)(color(red)(1)color(blue)(0)color(red)(9)0.00color(red)(1)0)`

The second, third, and fourth sandwiched zeros follow `color(red)(9)` and are followed by `color(red)(1)`. This means that your number contains

`color(black)(color(red)(1)color(blue)(0)color(red)(9)color(blue)(0). color(blue)(00)color(red)(1)0) -> " 4 sandwiched zeros: " {color(blue)(0), color(blue)(0), color(blue)(0), color(blue)(0) }`

Finally, you should know that trailing zeros, i.e. zeros that follow a non-zero digit and are not followed by a non-zero digit, that follow a decimal point are significant.

In this case, you have one trailing zero that follows the decimal point and the `color(red)(1)` that's in the thousandths place

`color(black)(color(red)(1)color(blue)(0)color(red)(9)color(blue)(0). color(blue)(00)color(red)(1)color(green)(0)) -> " 1 significant trailing zero: " {color(green)(0)}`

Therefore, you can say that your number has a total of

`color(white)(aaaaaaa)color(red)("3 non-zero digits") " "+`
`color(white)(aaaaa)color(blue)("4 sandwiched zeros")`
`color(green)("1 significant trailing zero")`
`color(white)(aaaaaaaaaaaaaaaaaaaaaa)/color(white)(a)`
`color(white)(aaaaa)"8 significant figures"`