1. The problem is to round the number 14.63 to the nearest integer. 2. To round a number to the nearest integer, look at the digit in the tenths place (the first digit to the right of the decimal point). 3. For 14.63, the digit in the tenths place is 6. 4. Since 6 is 5 or greater, we round the integer part up by 1. 5. The integer part of 14.63 is 14, so rounding up gives us 15. 6. Therefore, 14.63 rounded to the nearest integer is $15$.