Example
Estimate 699 + 710 + 695 + 705 + 694 + 715
Carefully examine all the numbers above. You should notice that they all cluster around 700
Therefore, 700 + 700 + 700 + 700 + 700 + 700 will give us a good estimate for the answer.
Instead of adding 700 six times, just do 6 × 700.
700 × 6 = 4,200 is a good estimate of the sum
In fact, the real answer 699 + 710 + 695 + 705 + 694 + 715 = 4,218. Thus 4,200 is indeed close to the real answer.
Example 2
Estimate 257 + 247 + 255 + 245
Carefully examine all the numbers above. You should notice that they all cluster around 250
Therefore, 250 + 250 + 250 + 250 will give us a good estimate for the answer.
Instead of adding 250 four times, just do 4 × 250.
250 × 4 = 1,000 is a good estimate of the sum
In fact, 257 + 247 + 255 + 245 = 1004. Thus 1000 is indeed close to the real answer.
Example 3
Estimate 23 × 18 × 22 × 17
Therefore, 20 × 20 × 20 × 20 will give us a good estimate for the answer.
Multiply the 2s to get 16.
Then, just put four zeros after 16 to get 160,000
The real answer is 23 × 18 × 22 × 17 = 154,836.
It is not a very good estimate, but we can live with that
In general, addition will give better estimates
Front Ends
Front-end estimation is a particular way of rounding numbers to estimate sums and differences. To use front- end estimation, add or subtract only the numbers in the greatest place value. Then add the decimals rounded to the nearest tenth.
Example
Estimate the sum using front-end estimation: 4.9+3.8+7.2
First, look only at the whole numbers and add the digits in the ones places.
4+3+7=14
Next, look at the decimals and round them to the nearest whole number.
0.9+0.8+0.2
0.9 is approximately 1
0.8+0.2=1
So 0.9+0.8+0.2 is approximately 2.
Then, add the two together.
14+2=16
Exercise 2
Estimate the difference using front-end estimation: 9.52−3.39
First, look only at the whole numbers. Subtract the digits in the ones places.
9−3=6
Next, look at the decimals and round them to the nearest whole number.
0.52−0.39
0.52 is approximately 0.5
0.39 is approximately 0.4.
So 0.5−0.4=0.1
Then, add the two together.
6+0.1=6.1
Exercise 3
6-0.1
substract the integer part 6-0=6
and substract the deicimals 0-0.1, but 0.1 it is rounded to 0 because it is the closest, so 0-0=0
and the total is the sum of the integer part and decimal, so
6+0=6
the aproximation of the substract is 6