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Z.6 Estimate products of decimals

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What does it mean to estimate the product of decimals?

Estimating the product of decimals means finding an answer that is close to the exact result by rounding each number before multiplying. Estimation helps us check if our final answer makes sense and allows us to solve problems quickly without using exact decimals.

Example:
  • 4.7 × 2.1 → Round 4.7 to 5 and 2.1 to 2 → 5 × 2 = 10
  • The estimated product is 10.
Note

Estimation gives you a reasonable answer, not the exact one. It helps you decide whether your precise calculation is correct.

Rounding decimals to the nearest whole number

Rounding decimals means finding the closest whole number to a decimal by looking at the digit in the tenths place.

Rounding Rules:
  • If the tenths digit is 5 or greater, round up to the next whole number.
  • If the tenths digit is less than 5, round down to the current whole number.
  • Example 1: 3.6 → round up to 4
  • Example 2: 7.3 → round down to 7
Note

Always check the tenths digit before rounding. Rounding helps make multiplication with decimals faster and easier to estimate.

Estimating by rounding both decimals

To estimate a product, round each decimal to the nearest whole number first, then multiply the rounded numbers.

Example:
  • 6.8 × 3.4 → Round 6.8 to 7 and 3.4 to 3 → 7 × 3 = 21
  • The estimated product is 21.
Note

This method gives a quick estimate of what the answer will be close to. It helps you check whether your calculator or long multiplication result is reasonable.

Estimating when one number is less than 1

When one decimal is less than 1, the product will be smaller than the other number. You can still round both numbers to estimate easily.

Example:
  • 0.8 × 5.2 → Round 0.8 to 1 and 5.2 to 5 → 1 × 5 = 5
  • The estimated product is about 5. The exact answer (4.16) is close to that.
Note

If a decimal is less than one, think of it as “part of a whole.” The product will usually be smaller than the whole number you multiply by.

Estimating when both decimals are less than 1

When both decimals are less than 1, the product will be smaller than either of the numbers. Rounding each to the nearest whole number may give 0 or 1, depending on their tenths digits.

Example:
  • 0.7 × 0.5 → Round both to 1 → 1 × 1 = 1
  • Even though the estimate is 1, the exact product (0.35) is much smaller. This shows estimation gives an approximation, not an exact match.
Note

When both numbers are less than 1, expect the real answer to be smaller than 1. Estimation still helps check reasonableness.

Using estimation to check reasonableness

After finding the exact product of decimals, use estimation to decide if your answer makes sense. If your result is much larger or smaller than your estimate, check your calculation again.

Example:
  • 3.9 × 2.4 → Estimate first: 4 × 2 = 8
  • Exact answer: 3.9 × 2.4 = 9.36
  • Since 9.36 is close to 8, your answer is reasonable.
Note

Always compare your estimate to your exact answer. Estimation is a great way to double-check your math work.