$0.23$

You have to round to one decimal place. Mentally divide the number into two pieces:

$0{.}2 \;\; 3$

Consider the first digit of the second part. This is the first digit to be omitted.

$0{.}2 {\color{red} 3}$

The digit under consideration is a 3. So it is rounded down. This means that the second part is cut off without changing the first.

$0.2$

$0{.}78$

You have to round to one decimal place. Mentally divide the number into two pieces:

$0{.}7 8$

Consider the first digit of the second part. This is the first digit to be omitted.

$0{.}7 {\color{red}8}$

The digit under consideration is an 8. So it is rounded up. This means that the second part is omitted and the last digit is increased by 1. The 7 becomes the 8.

$0{.}8$

$3{.}716$

You have to round to one decimal place. Mentally divide the number into two pieces:

$3{.}7 16$

Consider the first digit of the second part. This is the first digit to be omitted.

$3{.}7 \color{Red}16$

The digit under consideration is a 1. So it is rounded down. This means that the second part is cut off without changing the first.

$3{.}7$

$10{.}008548548484$

You have to round to one decimal place. Mentally divide the number into two pieces:

$10{.}0 08548548484$

Consider the first digit of the second part. This is the first digit to be omitted.

$10{.}0 \color{red}08548548484$

The digit under consideration is a 0. So it is rounded down. This means that the second part is cut off without changing the first.

$10{.}0$

$99{.}999$

You have to round to one decimal place. Mentally divide the number into two pieces:

$99{.}9 99$

Consider the first digit of the second part. This is the first digit to be omitted.

$99{.}9 \color{red}99$

The digit under consideration is an 8. So it is rounded up. This means that the second part is omitted and the last digit is increased by 1. Since it is a 9, you have to adjust several digits.

$100{.}0$

As you can see, "increasing" the 9 at the tenths place also results in an adjustment of the ones, tens, and hundreds.