Concept 6 of 7
Estimation of Products
Today's big idea
Round each number to the place named, then multiply the rounded values.
Different rounding places give different estimates, so the question must say which.
How it works
👀 What's going on?
A question asks roughly how much, and you start the long multiplication anyway. Rounding first gets you close enough in a single line.
💡 Here's the trick
Look at the numbers above. Round each one to the place the question names, then multiply the rounded values. The estimate lands near the true answer and takes a fraction of the time.
🪄 How to do it
- 1.Round each of the numbers above to the place the question asks for.
- 2.Multiply the rounded numbers.
- 3.Say whether your estimate sits above or below the true value.
✍️ Try it
Estimate 512 times 79, rounding each to the nearest ten. Then: estimate 397 times 62, rounding each to the nearest hundred and ten.
510 times 80 gives 40,800, and the exact answer is 40,448. Rounding the second pair to 400 and 60 gives 24,000, against an exact 24,614.
⚠️ Watch out
You might be thinking any rounding will do. The question has to say what to round to. Rounding 512 to the nearest ten gives a different estimate from rounding it to the nearest hundred, and both are right for their own instruction.
🌟 Why this matters
Checking a shopping bill or judging whether an answer looks sensible is estimation, and it catches mistakes exact working hides.
Exam tip: Estimate first, then compute; if the two disagree wildly, one of them is wrong.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Estimate 297 × 41 by rounding each number to the nearest 10.”
- 1
Round each number
297 → 300; 41 → 40.
- 2
Multiply rounded values
300 × 40 = 12,000
- 3
Answer ✓
12,000
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
To estimate a product: round each number to the nearest ten, then multiply the rounded numbers.
ESTIMATE · ROUND 1 OF 3
Estimate 78 × 53 by rounding to the nearest ten.
Quick check
✅ VERIFICATION
Estimate 6,120 × 39 by rounding each number to the nearest ten.
⚡ Finish the activity above first to answer.
Keep going!
Up next: Division Cryptarithms
Every line you subtract is the divisor times one digit.