Rounding — Definition, Formula & Examples
Rounding is replacing a number with a simpler, nearby number that is close to the original value. You choose a place value (like tens or hundreds) and adjust the number up or down based on the digit to the right.
Rounding a number to a given place value means replacing it with the nearest multiple of that place value. If the digit immediately to the right of the target place is 5 or greater, the digit in the target place increases by 1 (round up); if it is less than 5, the digit in the target place stays the same (round down). All digits to the right of the target place become zero.
How It Works
First, identify which place value you are rounding to (ones, tens, hundreds, etc.). Next, look at the digit one place to the right of that position — this is your decision digit. If the decision digit is 0, 1, 2, 3, or 4, keep the rounding digit the same and replace everything to the right with zeros. If the decision digit is 5, 6, 7, 8, or 9, increase the rounding digit by 1 and replace everything to the right with zeros.
Worked Example
Problem: Round 368 to the nearest hundred.
Identify the rounding place: The hundreds digit in 368 is 3.
Find the decision digit: The digit one place to the right of hundreds is the tens digit, which is 6.
Apply the rule: Since 6 is 5 or greater, round up: increase the hundreds digit from 3 to 4 and replace the remaining digits with zeros.
Answer: 368 rounded to the nearest hundred is 400.
Why It Matters
Rounding helps you estimate answers quickly — for instance, checking whether a grocery total of $4.87 + $3.12 is roughly $8. It is also essential when reporting measurements, since tools like rulers and scales have limited precision.
Common Mistakes
Mistake: Rounding down when the decision digit is exactly 5.
Correction: The standard rule is that 5 rounds up. For example, 350 rounded to the nearest hundred is 400, not 300.