The rounded number is 0.3.
It's important to understand that rounding to the place of the underlined digit involves examining the digit to the right of the targeted place.
If that digit is 5 or greater, rounding up is performed; otherwise, rounding down occurs.
In this case, the hundredths place is 4, and rounding down leads to the number 0.34.
To round the number 0.34 to the place of the underlined digit, we need to look at the digit to the right of the underlined digit, which is 4.
Since 4 is less than 5, we round the underlined digit down. Therefore, the rounded number is 0.3.