We deal with numbers in our life on a daily basis. Especially, people related to the education sector use them a lot.
Some numerical values contain so many digits that we find it difficult to use the “unit, tens, and hundreds” rule for knowing how big or small that number is.
To make this process of reading easy and convenient to use in calculations we convert such numbers into standard form.
The most common example of this is the speed of light. According to NASA, the speed of light is 299,792.458 kilometers per second.
Now, this is a HUGE number. It is difficult to read and even more difficult to use in the formulas.
To remove inconvenience such as mentioned above, scientists have come up with a standard form of numbers.
What is standard form?
A way of writing particularly very large or small numbers in a format of a10n.
For instance, the speed of light is written as 3 108km per second. It makes this easy for daily use.
How to convert numbers into standard form?
Converting numbers into standard form can be tricky. But with the right amount of practice, you will be able to do it the right way.
Let’s learn by an example, suppose we have a number 12300000000. You want to convert it into standard form. Here are the steps you’ll need to follow.
Add Decimal:
First and foremost we will add a decimal point to this number. The decimal point is placed after the first non-zero digit from the left.
In the case of our example, we will place it after the number 1. It will look like this:
1.2300000000
Count the number of digits after decimal place:
For the second step, you’ll need to count how many digits are written after the decimal point. No matter if they are zero or non-zero digits.
In our example, we have counted that there are 10 digits after the decimal place, starting from 2 on the right and ending on the zero at the leftmost side.
Raise the power to ten:
Now, raise the number you have counted as a power to 10 and multiply it to the value.
After doing this step, our example will be such as
1.2300000000 1010
Keep two digits after the decimal point:
Remove all the numbers after decimal except the first two. See if the fourth-place number is greater than 4 then round off the third-place (if 4 or less) number by adding 1 to it. But if it is 4 or some number less than 4, keep the same number.
In the case of our example, the fourth number is “0”. So we will keep the same number.
1.231010
Here is the final result of the process.
Positive and negative Exponents:
Positive exponents are of the numbers that are greater than zero while negative exponents are of the numbers that are less than zero.
The only difference between the conversions of negative numbers to standard form is that they were originally written with zero as the first digit.
And the power of ten is represented with a negative “-” sign.
The above-mentioned example is a positive exponent. An example of negative numbers would be
000000000546
I will convert this number without mentioning the steps.
- 46
- 46 10-9
The little difference here is the direction of counting. As the decimal is placed at not the first place but after the first non-zero digit.
So we start counting from the left to the right and stop just before the number after which the decimal point is placed.
In our example, we started from the rightmost zero and counted till the zero just before five.
Standard form calculator:
After reading all of these steps of converting normal numbers into standard form, you would have realized it’s a time taking process.
And most of the time, we need them in standard form as fast as possible.
For this purpose, there are many online numbers to standard form converting calculators which would do the difficult work for you.
One such calculator is the mera calculator. I‘ve personally used it. I like this calculator because not only it gives you the result in standard form but also tells you the real numbers, e- notation, and engineering notation.
Popular examples:
Many values that we study in science are already converted into standard form. One of them is the speed of light which I already mentioned.
Some others are:
- The distance between the sun and the earth is 1.42108miles.
- The masses of electrons, protons, and neutrons are 9.1110-31and 1.6710-27kgrespectively.
- The average size of blood cells is 1.5 10-5m.
