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why can you estimate a quotient without completing the division?
2 answers
If you are doing the long division, you get closer to the correct answer the more decimal places you carry it out. You do not have to "complete" the division.
Another way to get an answer "in your head" is by memorizing a few relationships like 1/2 = 0.500, 3/8 = 0.375 and 0.714 = 5/7 etc.
Take a look at the quotient and try to approximate or "bracket" it with a fractions with smaller integers. Then use the relationships you have memorized.
Here's an example: 23/87
That is more than 1/3 (23/69 = 0.33) and less than 1/4 (23/92 = 0.25) but closer to 1/4. I would guess the answer to be 0.27
The correct answer is 0.264
Another way to get an answer "in your head" is by memorizing a few relationships like 1/2 = 0.500, 3/8 = 0.375 and 0.714 = 5/7 etc.
Take a look at the quotient and try to approximate or "bracket" it with a fractions with smaller integers. Then use the relationships you have memorized.
Here's an example: 23/87
That is more than 1/3 (23/69 = 0.33) and less than 1/4 (23/92 = 0.25) but closer to 1/4. I would guess the answer to be 0.27
The correct answer is 0.264