Approximation in Mathematics simply means making a rough estimate of a particular figure to the particular digits as requested by an examination or as required in a particular problem solving.
Approximation in Mathematics is majorly divided into two different parts such as round up and round down or round off.
Each number in arithmetic would be either be rounded down(off) or up depending on the number in question.
Take for instance, you were told to approximate a particular number; 7.85 to the nearest whole number.
A whole number is a single number with no decimal points or fraction.
Such as; 15,68,98,109 and so on.
7.85 can be approximated 8
This is so because the last digit in 7.85 which is 5 is a number that is rounded up.
Now let's talk on rounding up;
Rounding up means approximating a number to 1 and adding it to the next number to make it 1 and then adding it to the next number to become increased by 1.
Any number from 5 to 9 is rounded up and not rounded off or down
Such as 7.86
If this number is a round up to 1 decimal place it becomes 7.9 as the final answer.
Also 76.98 becomes 77 in nearest integer or whole number fraction.
Moreover, 66.9358
It becomes 66.936 when rounded up to 6 decimal places.
Now, let's proceed to round down or round off as it may called in some textbooks.
In arithmetic generally, any number ranging from 0 to 4 is rounded off or down as the case may be.
Take for instance, approximate 7.539 to 1 decimal place;
Moreover, estimate 68.24cm to the to cm unit leaving out the decimal fraction
Approximating this number it would become 68cm to the nearest cm
Last but not least, approximate 143.2315 to 2 decimal place.
The final solution would be 143.23 to 2 decimal place as approximating the last number in 143.2315 which is 5 would make 1 become 2 and approximating 2 it becomes zero and has no effect on 3 which makes it remains the same which happens to be the second number after the decimal point to the right side and as such the final solution is ; 143.23 to 2 decimal place
That's as regards the approximation atleast for now. In the subsequent posts more would be discussed on place value of different digits in different figures both before and after the decimal point fractions whether positive or negative numbers.
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