Question

Express 3430000 in the standard form.

Answer 1

Hint: To write the number in standard form, take the decimal at the place just next to the greatest place value digit and the number of places you have jumped to take the decimal to that place is written as the exponent of 10.

Complete step-by-step answer:

First we have to understand, what is the meaning of writing a number in standard form? A standard form is a way of writing down very large or very small numbers easily. For example: ${{10}^{4}}=10000$, so $5\times {{10}^{4}}=50000$. Therefore, 50000 can be written as $5\times {{10}^{4}}$. This idea can be used to write even large numbers in standard form easily.

Small numbers can also be written in standard form. However, instead of the index being positive, it will be negative. Let us take a few examples. We have to write 534490000 in standard form. So, $534490000=5.3449\times {{10}^{8}}$, it is ${{10}^{8}}$ because the decimal point has been moved 8 places to the left to get the required standard form. Let us take another example, to write 0.000045 in standard form. So, $0.000045=4.5\times {{10}^{-5}}$, it is ${{10}^{-5}}$ because the decimal point has been moved 5 paces to the right to get the required standard form.

Now, let us come to the question. We have been provided the number, 3430000. Therefore, the standard form is, $3430000=3.43\times {{10}^{6}}$, here, we have moved 6 places to the left.

 Hence, the standard form of 3430000 is $3.43\times {{10}^{6}}$.

Note: It is important to note that the standard form of representing numbers is also called scientific form or standard index form. Those numbers that are too big or too small are written in standard form to make calculations easy.