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A standard form calculator helps in performing mathematical operations when the numbers are expressed in scientific notation. People who do not have a mathematics background can use these tools and eliminate unnecessary stress. To use these tools, you have to enter the numbers in standard form and select the operation to be performed. This quality tool would provide you with the correct results. It is an option that does not involve the hassle of writing down the solution steps and then getting to the answer.
What is standard form?
Before you start using a standard form calculator, it is good to have basic information about what standard form is. It is a method of expressing numbers as a power of ten. If you are dealing with very small numbers (0.025), they can be expressed as a power of ten. However, the power would be negative. Similarly, large numbers (4000) can be expressed as a positive power of ten.
- The number \(0.025\) would be written as: \(2.5 \times 10 - 2\)
- The number \(4000\) would be written as: \(4\times103\)
Decimal numbers have small values. Hence, when you are converting them to standard form, the power of ten is negative. Similarly, when you are converting a large number to standard form (scientific notation), the power of ten would be positive.
Standard Notation Calculator
The term standard notation is another term for standard form. When a number is represented in standard notation, it is broken down and represented as a power of ten. Consider that you have the number 4987. This number “4987” in its current form is called expanded notation. To convert it into the standard form, you need to portray it as a power of 10.
\(4987\) would be given as
\(4987 = (4 \times 103) + (9 \times 102 ) + (8 \times101) + (7 \times100)\)
\(4987 = 4000 + 90 + 80 + 7\)
\(4987 = 4987\)
In accordance with the expression shown above, the left hand and right-hand sides are equal. Hence, the standard notation is correct.
Is it better to use this standard notation calculator? There is no doubt that users get a lot of relief after using this tool. They do not have to spend time writing the steps, inserting values and then producing the results. If you don’t have a strong base of statistics, completing all these steps would become hard for you. This is a dependable tool that comes with an easy interface.
Convert to standard form
As has been explained above, the standard form is the expression of a number as a power of 10. If you need to represent the number 5688 in standard form, the following steps would be performed.
\(5687 = (5\times103 ) + (6\times102)+ (8\times101) + (7\times100 )\)
Interpretation of the steps
To convert a number to the standard form, it is important to understand the process properly in a stepwise manner. Here are some steps which explain the conversion process to standard form.
- A number is broken down into powers of ten from maximum to minimum. If you have a look at the number above, the maximum power is thousand. The digit has the power of a thousand. The power of thousand is represented as 10 raised to the power 3. Similarly, the digit 6 represents “hundred” so it is shown as 10 raised to the power 2. The digit 8 represents “tens”. Thus, it is displayed as 10 raised to the power 1. Finally, “units” is represented by 7 so it is displayed with 10 raised to the power 0. Anything raised to the power 0 has a value of 1.
- To confirm that the standard form is correct, add the components to get a confirmation. If the sum is equal to the actual number, it means that the process of breaking done is correct.
Performing mathematical operations in standard form
Displaying a number in standard form may not be that hard one has to be careful when mathematical operations have to be performed. Consider that you have to multiply the following numbers after converting them in standard form.
\(4000 \times 8500\)
Converting \(4000\) to standard form, it would be given as
\(4 \times 103\)
Similarly, \(8500\) would be given as
\(8.5 \times 103\)
Now, let us multiply both these standard forms to get the final result
\(4 \times 8.5 \times 103 \times 103\)
\(34 \times 106\)
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