Definition

Approximation
When solving a math problem, approximating the answer first serves as a check as to whether your actual answer is correct or not. We use rounding off to obtain an approximation to the actual value.

Rules for rounding off:
1. Look at the digit to the right of the specified place.
2. If the digit is less than 5, replace it and all the digits to its right by zeros.
3. If the digit is 5 or more, add 1 to the digit in the specified place and replace all the digits to its right by zeros. 

e.g. 2385 ≈ 2390 (correct to the nearest 10)
       2384 ≈ 2380 (correct to the nearest 10)

Likewise, when rounding off a number to a given number of decimal places, 
1. Include one extra digit for consideration.
2. Drop the extra digit if it is less than 5.
3. If it is 5 or more, add 1 to the previous digit before dropping the extra digit.

e.g. 9.635 ≈ 9.64 (correct to 2 d.p.)
       9.633 ≈ 9.63 (correct to 2 d.p.)

Significant Figures

Some things to note: 
1. Zeros between non-zero digits are significant.
2. Zeros preceding the first non-zero digit are not significant.
3. Zeros following a non-zero digit after the decimal point are significant.
4. Zeros following a non-zero digit in a whole number may or may not be significant. e.g. if 6200 is written correct to 4 s.f., then all the zeros are significant.

When rounding off a number to a given number of significant figures,
1. Count the given number of significant figures from left to right, starting with the first non-zero digit. Include one extra digit for consideration.

2. If the extra digit is less than 5,
(a) drop the extra digit and all the other digits to its right, or
(b) replace the extra digit and all the digits to its right by zeros to keep the place value. 

For example, for (a), 1.524 ≈ 1.52 (to 3 s.f.)
                          (b), 7300 ≈ 7000 (to 1 s.f.)

3. If the extra digit is 5 or more, 
(a) add 1 to the previous digit before dropping the extra digit, or
(b) replace the extra digit and all other digits to its right with zeros to keep the place value.

For example, for (a), 2.356 ≈ 2.36 (to 3 s.f.) 
                          (b), 6281 ≈ 6300 (to 2 s.f.)

Definition

To estimate a calculation, round off each number to the number of significant figures as necessary and estimate from there. 

TIP!
To estimate to 1 s.f., estimate to 2 s.f. in the working and then round off to 1 s.f. in the final answer. Remember to work to one s.f. more than required in the final answer. 

Rounding and Truncation Error

Calculators do not always give the exact answers. This happens because the number of digits stored and used for calculation depends on the capacity of the calculator. 
These type of errors are called rounding and truncation errors. 
E.g. when we use the calculator to evalute 2 ÷ 3, we get either 0.666...667 (rounding) or 0.666....66 (truncation)

Video Example

Watch the following video for further examples of how this is done: