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In positional notation, significant figures are reliable digits in a number that are required to denote the amount of something. Significant numbers consist of meaningful digits that are known, plus one that is approximated or uncertain. Certain numerals and the final uncertain digit are used to denote the uncertainty. For example, 0.0025 has 2 significant figures. In a number, the zeros written to the left of the first non-zero digit are insignificant. They simply display the decimal point's location.
Every digit that is not zero is significant. There are 2 significant digits in the number 0.0025.
Between any two non-zero digits, all zeros are significant. For example, 102.0876 has seven significant digits.
Any zeros present to the left of a non-zero digit and to the right of a decimal point are non-significant. For example, the value 0.0025 has two significant digits.
They are considered significant only if a non-zero digit does not come after any of the zeros to the right of a decimal point. For example, 300.00 has five significant digits.
After the decimal point, all the zeros to the right of the last non-zero digit are significant. For instance, 0.002500 has four significant digits.
If a measurement is involved, all of the zeros to the right of the last non-zero digit are significant. For example, the number 2070 m has four significant digits.
A number is rounded off by excluding one or more digits from the right, bringing it to the required number of significant digits. There are well-established guidelines for rounding off. Let's decide what to call the various parts of a numerical value before we write them out.
The leftmost digit is the most significant one (not counting any leading zeros which only act as placeholders and are never considered significant digits.)
The least significant digit is the nth digit from the most significant digit if you are rounding off to n significant digits. A zero may be used as the least significant digit.
The (n+1)th digit is the first non-significant digit.
The significant numbers should be rounded off according to the following rules:
The least significant digit remains the same if the first non-significant digit is less than 5. For example, if we have to round up 1.583 to 3 significant digits, in this case, 8 will be the least significant digit and 3 will be the first non-significant digit. As 3 is less than five, thus 1.583 will be rounded off as 1.58.
The least significant digit is increased by 1 if the first non-significant digit is greater than 5. For example, if we have to round up 1.568 to 3 significant digits, in this case, 6 will be the least significant digit and 8 will be the first non-significant digit. As 8 is greater than 5, therefore 1.568 will be rounded off as 1.57.
When the first non-significant digit is equal to 5 then also we add 1 in the least significant digit. For example, if we have to round up 1.545 to 3 significant digits, in this case, 4 will be the least significant digit and 5 will be the first non-significant digit. As the first non-significant digit is equal to 5, therefore 1.545 will be rounded off as 1.55.
Solve the following 3.26 + 2.62 + 44.21 and find the number of significant digits/figures.
Ans: After solving, we will get,
3.26+2.62+44.21=50.09
Hence, there will be 4 significant figures in 50.09.
Identify the number of significant figures in 1.560.
There are 4 significant figures in 1.560.
Write 11.56893 correct to 4 significant digits.
The number 11.56893, rounded to 4 significant digits, is 11.57. Hence the correct answer is 11.57.
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