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E.2 Divide numbers ending in zeros

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What are division problems with ending zeros?

Dividing numbers ending in zeros is a mathematical process where both the dividend (number being divided) and/or the divisor (number dividing by) end with one or more zeros. Special strategies make these problems easier to solve.

Examples:
  • 350 ÷ 5
  • 4,200 ÷ 60
  • 81,000 ÷ 900
Note

When numbers end with zeros, we can simplify the division by temporarily removing the zeros and then adding them back to our answer.

The zero-removal strategy

When both dividend and divisor end with zeros, you can remove the same number of zeros from both numbers before dividing.

Steps:
  • Identify how many zeros you can remove from both numbers
  • Remove the same number of zeros from both dividend and divisor
  • Divide the remaining numbers
  • Your answer is the quotient of the simplified numbers
Note

You can only remove zeros when both numbers have zeros to remove. Always remove the same number from both.

Dividing when only the dividend has ending zeros

When only the dividend ends with zeros, you can still simplify by removing zeros, but you must add them back to your quotient.

Example:
  • 2,400 ÷ 8
  • Remove two zeros: 24 ÷ 8 = 3
  • Add two zeros back: 300
  • So 2,400 ÷ 8 = 300
Note

When only the dividend has ending zeros, remove them before dividing, then add the same number of zeros to your answer.

Dividing when both numbers have ending zeros

When both dividend and divisor end with zeros, remove the same number of zeros from both, divide, and your answer is complete.

Example:
  • 6,300 ÷ 90
  • Remove one zero from both: 630 ÷ 9
  • Divide: 630 ÷ 9 = 70
  • So 6,300 ÷ 90 = 70
Note

When both numbers have zeros, you don't need to add zeros back to your answer because you've already simplified proportionally.

Checking your work

Always verify your division answer by using multiplication. Multiply your quotient by the divisor to see if you get the original dividend.

Example:
  • Problem: 4,800 ÷ 60 = 80
  • Check: 80 × 60 = 4,800
  • Since 80 × 60 = 4,800, our answer is correct
Note

Multiplication is the inverse operation of division. Using it to check your work helps catch errors.

Common patterns to recognize

Recognizing patterns in division with zeros helps you solve problems more quickly and accurately.

Pattern Examples:
  • Any number divided by 10: remove one zero (350 ÷ 10 = 35)
  • Any number divided by 100: remove two zeros (7,200 ÷ 100 = 72)
  • When dividend has more zeros than divisor: remove matching zeros, then add back extras
Note

Practice recognizing these patterns to become faster at mental math with division problems.