What are Scientific Notations?
A scientific notation is a form of writing a given number, an equation, or an expression in a form that follows certain rules. In other words, Scientific notation is the standard way to express a number as the product of a real number and power of 10.
How do we define scientific notation in mathematical form?
Now that we know about the basic definition of the scientific notation, let us move to understand the mathematical definition of a scientific notation.
Scientific notation is defined as a standardized way to represent any number as the product of a real number and a power of 10. This means that in a scientific notation, a number is written in the form of a x 10 b where a is called the coefficient and b is the exponent.
Let us understand this by an example.
Suppose we have a number 70.
We multiply it by 10 to get 700.
We again multiply 700 by 10 to get 7000
Next, we again multiply 7000 by 10 to get 70000.
We can see that the number is getting larger and larger as we keep on multiplying it by 10.
Instead of writing this number in the larger number format, we can write it down as
70 = 7 x 10 = 7 x 10 1
700 = 7 x 100 = 7 x 10 2
7000 = 7 x 1000 = 7 x 10 3
70000 = 7 x 10000 = 7 x 10 4
In the above four examples, 7 is the coefficient and 1, 2, 3 and 4 are the exponents respectively.
What are Significant Figures?
Significant figures refer to the number of important single digits (0 to 9 inclusive) in the coefficient of expression in the scientific notation. Below are some important rules pertaining to significant figures –
- All non-zero numbers are significant. For instance, the number 48.7 has three significant figures because all of the digits present are non-zero.
- Zeros between two non-zero digits are significant. For instance, 4078 has four significant figures as the zero is between a 4 and a 7.
- Leading zeros are not significant. This means that the leading zeros are just like placeholders. For instance, the number 0.78 has only two significant figures. Similarly, 0.0064 also has two significant figures. All of the other zeros are leading.
- Trailing zeros to the right of the decimal are significant. For instance, there are four significant figures in 36.00.
- Trailing zeros in a whole number with the decimal shown are significant. It is not usually done that we place a decimal at the end of a number. However, such a decimal indicates a significant zero. For example, the number 480. indicates that the trailing zero is significant; therefore, there are three significant figures in this number.
- Trailing zeros in a whole number with no decimal shown are not significant. This means that writing 670 indicates that in this case, the zero is not significant, and therefore, there are only two significant figures in this value.
- Exact numbers have an infinite number of significant figures. This rule applies to numbers that are meant for the purpose of definitions. For example, 1 km = 1.00 km = 1.0000 km = 1.000000000000 km etc.
Let us now see how to use the significant figures calculator.
How to use the significant figures calculator?
It is quite simple to use the significant figures calculator to find the significant figures of a number. Below are the steps that should be followed for this purpose –
Step 1 – This calculator works on finding the significant figures of a number if we input any number in it. Below is the snapshot of how the display would be like as soon as we land on the significant figures page –
Step 2 – The first step is to enter the number for which we want to know the significant figures. For this purpose, we need to enter the number in the “ Enter Number “ section of the significant figures calculator. Let us take the number 658.12070 and see how we can obtain the significant digits of this number. We shall have to enter this number in the “ Enter Number “ section of the significant figures calculator. Below is a snapshot of how the number would be entered in the significant figures calculator –
Step 3 – The third step is to let the significant calculator know up to how many digits we want the significant figures to round off the number. Recall that rounding off a number is a type of estimation where a number is made simpler by keeping its value intact but closer to the next number. It can be done for whole numbers as well as for decimals. Let us suppose we wish it up to 3 digits. We shall, therefore, enter 3 in the section “Round to sig fig”. below is a snapshot on how to enter the same in the significant figures calculator –
Step 4 – Now that we have entered all the information that was required by the calculator to perform the operations, it is time for the calculations. Therefore, the next is to calculate the significant figures of the entered number. For this purpose, we just need to click on the “ calculate “ button. As soon as we will click on this button, we can see the result obtained on the right-hand side of the values that we had entered in the previous steps. Below is a snapshot of how the selection would look like when we will click on the “ calculate “ button –
Let us check what all information and calculation has been provided to us by the significant figures calculator –
Number of significant digits – This shows the number of significant digits of the given number.
Number of Decimals – This shows the number of decimals in the given number.
Significant Number – This shows the significant digits of the given number
Decimal Numbers – This shows the list of decimal numbers of the given number
E-notation – This shows the exponential form in which the given number can be expressed.
Scientific notation – This shows the Scientific notation in which the given number can be expressed.
Decimal notation – This shows the decimal notation of the given number.
In this manner, this significant figures calculator can be used to not only the significant figures of a number but also can be used to check how a number can be expressed in different notations, be it scientific, decimal or exponential forms.