Question

How do you convert ${\text{278,000}}$ into scientific notation?

Answer 1

Hint: Scientific notation is a method of expressing the very large or very small number in a compact form. One can write the above-given number in a compact form as taking only one decimal form of that number.

Complete step by step answer:
1) First of all, we will learn about the scientific notation concept. Scientific notation is the way for expressing a very large number or a very small number in a very short or compact form. The way to write in a compact form is to take that number to only one decimal point and the remaining value is taken in terms of the power of the ten.
2) Now let us take the number which is given in the question and convert it into a scientific notation as below,
${\text{278,000}}$
This number has a total of six digits in it and we need to convert them into the only digit.
3) So, to convert it into a single digit we need to move the dot from the last digit to the location after the digit. We can do this as below,
${\text{278,000 = 2}} \cdot {\text{78000 }} \times {\text{ 100000}}$
4) Now we can take the value of ${\text{100000}}$ in terms of tenth power as below,
${\text{100000 = 1}}{{\text{0}}^5}$
As the number has zero values after the one value, the tenth to the power value is in a positive value.
5) Therefore, we can write the conversion of ${\text{278,000}}$ into a scientific notation form as ${\text{2}} \cdot {\text{78 }} \times {\text{ 1}}{{\text{0}}^5}$.

Note:
While writing the scientific notation one must remember to take only one decimal number and the rest can be taken as a power to the ten. The power value goes negative if there are zeros behind a number and it goes positive if there are zeros after a number.