A magnitude estimate says which range an answer falls into: the tens, the hundreds, the thousands, and so on. It is deliberately rough. Its job is to catch the errors that change the size of an answer rather than its last digit, and those are the errors that matter most.
Making one
- Round each number to one significant digit, so 38 becomes 40 and 612 becomes 600.
- Do the easy calculation with those.
- Name the range the result sits in.
Magnitude estimate for 38 x 612
38 x 612 about 40 x 600 = 24,000 magnitude: ten-thousands
An exact answer of 23,256 fits. An answer of 2,325 or 232,560 does not, and both are what a misplaced decimal point or a lost zero looks like.
What it catches
| Candidate answer | Estimate says | Verdict |
|---|---|---|
| 2,325 | should be near 24,000 | ten times too small, a digit was lost |
| 23,256 | should be near 24,000 | plausible |
| 232,560 | should be near 24,000 | ten times too large |
| 23,256,000 | should be near 24,000 | wildly wrong |
Estimating a quotient
Magnitude estimate for 4,812 / 61
about 4,800 / 60 = 80 magnitude: tens
So an answer in the hundreds would be wrong. The exact quotient is 78 with a remainder, which sits comfortably in the tens.
Common mistakes
Trying to be accurate
Rounding 612 to 610 instead of 600 makes the mental arithmetic harder and buys nothing. A magnitude estimate is allowed to be twenty percent off.
Estimating after seeing the answer
An estimate made after the fact tends to agree with whatever is already written down. Estimate first, then calculate.
Check yourself
Magnitude estimate for 78 x 43.
About 80 x 40 = 3,200, so the thousands. The exact answer is 3,354.
Magnitude estimate for 5,940 / 29.
About 6,000 / 30 = 200, so the hundreds.
A student writes 4.7 x 82 = 3,854. Is that plausible?
No. The estimate is about 5 x 80 = 400, so the answer should be in the hundreds. The student has multiplied 47 by 82 and lost the decimal point. The correct answer is 385.4.
Why round to one digit rather than two?
Because the point is speed and size, not accuracy. One-digit numbers can be multiplied in your head, and a magnitude estimate only has to be right about the range.
See also
Sources
- Magnitude estimation is introduced in Everyday Mathematics as a check on the size of a computed answer. Examples on this page are our own.