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D.3 Multiply whole numbers ending with zeros: word problems

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Understanding multiplication with zeros at the end

Multiplying whole numbers ending with zeros means finding the product of numbers that have one or more zeros at the end, such as 30 × 400. You can simplify the problem by ignoring the zeros first, then adding them back to your answer at the end.

Example:
  • 30 × 400
  • Ignore the zeros: 3 × 4 = 12
  • Count the zeros (3 in total) and add them to the product: 12,000
  • So, 30 × 400 = 12,000
Note

When both numbers end with zeros, multiply the nonzero digits first, then add all the zeros from both numbers to your final answer.

Why this works

Zeros at the end of a number show that the number is being multiplied by 10, 100, or 1,000, and so on. When you multiply numbers with zeros, you are really multiplying by powers of ten, which shift the digits to the left.

Example:
  • 20 × 300 = (2 × 10) × (3 × 100)
  • Group the factors: (2 × 3) × (10 × 100)
  • 6 × 1,000 = 6,000
  • So, 20 × 300 = 6,000
Note

Each zero represents a place value. Multiplying by 10 moves every digit one place to the left. Multiplying by 100 moves every digit two places, and so on.

Solving word problems with numbers ending in zeros

Word problems that include numbers ending with zeros require understanding what the problem is asking and using place value reasoning to find the correct product.

Example:
  • A farmer packs 20 boxes of apples. Each box holds 300 apples. How many apples does the farmer have in total?
  • Multiply: 20 × 300
  • Ignore zeros first: 2 × 3 = 6
  • Add the zeros (three in total): 6,000
  • Answer: The farmer has 6,000 apples.
Note

Always check that your answer makes sense. Estimate first by rounding to the nearest basic numbers before multiplying. This helps confirm that your product is reasonable.

Checking your work

After solving a multiplication problem with zeros, you can check your answer by dividing the product by one of the factors. The quotient should equal the other factor if your work is correct.

Example:
  • Check 40 × 600 = 24,000
  • Divide 24,000 ÷ 600 = 40
  • Since the quotient matches one of the factors, the answer is correct.
Note

Double-check zeros carefully when writing your answer. One missing or extra zero can change the value by a large amount.