Significant Figures are the digits of a number which are used for expressing the necessary degree of accuracy that starts from the first non-zero digit.
Examples of Significant Figures
“Significant figures is the number of digits in a number that actually convey any meaning. This does not include any information on the order or power of ten in the number representation, as this can be conveyed by other means.”
The term "significant figure" refers to the number of digits in a written number that can be trusted by implication. Factors that can reduce trust include the possibility of round-off errors and any explicit expression of uncertainty. Unless specified otherwise, all digits in a written number are considered significant. Also, whole numbers generally have an infinite number of significant figures unless uncertainty is expressed explicitly.
There are few simple rules for significant figures
- All non-zero digits are considered significant figures. For example, 345 has three significant figures.
- All zeros between non-zero digits are significant. Ignore the decimal point, if necessary. For example, the number 305 also has three significant figures. So does 3.05, because the zero is between non-zero digits.
- Zeros at the beginning of a decimal number or at the end of a large number are not significant. For example, 546,000 has only three significant figures. The three zeros simply serve to put the 5 in the 100,000s place, and the 6 in the 1000s place.
- Zeros written at the end of a number after the decimal point are significant. Otherwise, they would not even be written. For example, 0.67 has two significant figures, but 0.670 has three significant figures. If that final zero were not significant, it should not have been written down.
When adding significant figures (including negative numbers), the rule is that the least accurate number will determine the number reported as the sum. In other words, the number of significant figures reported in the sum cannot be greater than the least significant figure in the group being added.
Examples on Adding Significant Figures
Given below are some examples on adding significant figures.
Add the following numbers
446mm + 185.22cm + 18.9m.
First convert the quantities to similar units, which in this case is the mater (second row below). Next, choose the least accurate number, which s 18.9. It has only one number to the right of the decimal so the other two values will have to be rounded off (third row below).
|| Converted values
Answer = 0.4 + 1.8 + 18.9 = 21.1m
Add 5.80 and 3
We can round off the answer as 9. Therefore, 5.80 + 3 = 9
When the number is subtracted, the number of decimal places in the result should equal the smallest number of decimal places of any term.
The least significant digit of the difference occupies the same relative position as the least significant digit of the quantities being subtracted. In this case the number of significant figures is not important; it is the position that matters.
Examples on Subtracting Significant Figures
Given below are some examples on subtracting significant figures.
Subtract: 31.2 - 5.56
So, 31.2 - 5.56 = 25.64
Subtract: 72.2 - 3.56
So, 72.2 - 3.56 = 68.64
For addition and subtraction the important consideration is the number of decimal places, not the number of significant figures.
- The product or quotient should contain the number of significant digits that are contained in the number with the fewest significant digits.
- The number of significant digits in a product or quotient is the same as that in the least significant of the values used to calculate the product or quotient.
Examples on Multiplying Significant Figures
Given below are some examples that explains multiplication of significant figures.
Solve 16 x 35.6
The product of 16 x 35.6 = 569.6 has only two significant digits since 16 is the least significant of the values used in forming the product.
The product should be written as 16 x 35.6 = 57.
However, if it were predetermined that 16 was an integer good for an infinite number of decimal places, the product would have three significant figures based on the value 35.6.
The product would be correctly written as 16 x 35.6 = 570. In significant figure multiplication, the result must have as many significant digits as those of the number with the least significant digits entering the operation.
Solve 11.63 x 5.74
The product of 11.63 x 5.74 is 66.7562. But, according to the rules of multiplication in significant figures, the product must have only 3 significant figures. Therefore, the answer is 66.8.
11.63 x 5.74 = 66.8
Examples on Dividing Significant Figures
Given below are some examples on dividing significant figures.
Step 1: First convert the divisor into a whole number by moving the decimal point two places to the right, so that 2.66 becomes 266. Equalize this by moving the decimal point in the dividend the same number of places to the right, so that 3.795 becomes 379.5.
Step 2: Now proceed as in ordinary division but place the decimal point in the answer immediately after bringing down the first figure in the decimal.
Step 4: If the answer is required to the third decimal place, and the division is still not complete, then it should be carried to the fourth place.
Step 5: If the fourth figure is less than 5 it is ignored; if it is 5 or over, then 1 is added to the third place to obtain the nearest correct answer to the third decimal place.
Rules for Rounding Significant Figures
It is usual to round-off numbers according to the following rules:
- When a figure less than five is dropped, the next figure to the left remains unchanged. Thus the number 11.24 becomes 11.2 when it is required that the four be dropped.
- When the figure is greater than five that number is dropped and the number to the left is increased by one. Thus 11.26 will become 11.3
- When the figure that needs to be dropped is a five, round off to the nearest even number. This prevents rounding bias. Thus 14.25 becomes 14.2 and 57.75 becomes 57.7
Given below are some practice problems on significant figures.
Practice Problem 1:
Round to the correct decimal position
- 23.4 x 42.87 =
- 8.56 x 39.2 =
- 146 x 15.58 =
- 1.4756 x 2.4 =
- 3.4 x 4.21 x 1.8 =
- 7.34 / 4.9 =
- 24 / 4.34 =
- 5.3214 / 3.87 =
If a scale says a person weighs 182 pounds, how many kilograms(counting significant digits) is that person?