Question

How do you write 314,207 in standard form ?

Answer 1

Hint: Sometimes, it is very difficult to read numbers like 657964554454540000 or 0.000006546466. To make it easy to read very large and small numbers, we need to write them in standard form. Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in the standard form. \[2.594\times {{10}^{6}}\] and \[0.561\times {{10}^{-9}}\] are the examples of numbers in the standard form.

Complete step by step answer:
Standard form requires only one digit before the decimal.
Therefore, we will write the first number 3 and add a decimal after it. After that, we will put the numbers which are put in the number 314207 after 3.
So, we will write 314,207 as 3.14207.
Now, count the number of digits after 3. They are 5 digits.
So, as we have shifted the decimal to left by 5 places, we just need to multiply it by \[{{10}^{5}}\] to make them equal.

So, the standard form of \[314207\] can be written as \[3.14207\times {{10}^{5}}\].

Note: This type of problem is based on the real life examples. For example, if the distance between the Sun and the Mars is 141,700,000 miles or 228,000,000 km. This distance can be easily written in the standard form as: \[1.478\times {{10}^{8}}\] miles or \[2.28\times {{10}^{8}}\] km. But, some students can make mistakes in this question. Someone can write the standard form of 314207 as \[31.4207\times {{10}^{4}}\] . So, this will be the wrong way to solve the problem. Because, we just have to add decimal after the first number.