Mathematics Topic
Approximation and Estimation
- Read notes
- Flashcards
- Quiz
- Confident
Study focus - 3 things
- Approximation means using a close value that is easier to work with
- Rounding can be done to whole numbers, decimal places, or significant figures
- Estimation helps you check if a calculator answer makes sense
Section 1What approximation is
Approximation means replacing an exact value with a close value. Here's the trick: approximate values are easier to calculate with, but they are not exact. In exams, words like 'estimate', 'approximately', and 'to the nearest' tell you rounding is needed.
Section 2Rounding rules
To round, look at the digit after the place you are rounding to. If it is 5 or more, round up. If it is less than 5, keep the digit the same.
Section 3Decimal places and significant figures
Decimal places count digits after the decimal point. Significant figures count important digits from the first non-zero digit. Easy to mix up - 0.00482 to 2 significant figures is 0.0048, not 0.00.
Section 4Estimation to check answers
Estimation is a quick reasonableness check. If lunch costs J$485 and taxi fare is J$320, you can estimate J$500 + J$300 = J$800. If your calculator says J$80, something went wrong.
Examples
Round 47.86 to 1 decimal place.
One decimal place keeps the tenths digit: 47.8. The next digit is 6, so round up to 47.9.
Estimate 398 x 21 for a quick check.
Round 398 to 400 and 21 to 20. Then 400 x 20 = 8000, so the exact answer should be close to 8000.
Now let's water it
Session runs notes to flashcards to quiz back-to-back.