Question

How do you write 450,000,000 in scientific notation?

Answer 1

Hint: This problem deals with writing the given number in scientific notation form. To do this we need to choose a power of 10 that the mantissa lies in range. The definition of a mantissa is the part of a number located after a decimal point. Given a number which is in decimal form, the integral part of the number which is before the decimal is the characteristic whereas after the decimal is the mantissa.

Complete step-by-step solution:
Given a number 450,000,000, we are asked to write this in its scientific notation.
The purpose of scientific notation is for scientists to write very large, or very small numbers with ease.
Calculating scientific notation for a positive integer is simple, as it always follows this notation:
\[ \Rightarrow a \times {10^b}\]
To find $a$, take the number and move a decimal place to the right one position.
The given number is 450,000,000
Let the new number be 4.50000000
Here $a = 4.5$
$\therefore a = 4.5$
Now to find $b$, count how many places to the right of the decimal.

New number	4	.	5	0	0	0	0	0	0	0
Decimal count			1	2	3	4	5	6	7	8

Here there are 8 places to the right of the decimal.
$\therefore b = 8$
We can now reconstruct the number into scientific notation, as the notation is :
$ \Rightarrow a \times {10^b}$
We know that $a = 4.5$ and $b = 8$, hence substituting these in the general scientific notation:
So the scientific notation of the given number 450,000,000 is given below:
$ \Rightarrow 4.5 \times {10^8}$

450,000,000 in scientific notation is $4.5 \times {10^8}$

Note: Please note that we can verify by expanding the scientific notation we get the same original number. Here mantissa is also called significand where it is a part of a number in scientific notation or a floating point number, consisting of its significant digits. Depending on the interpretation of the exponent, the significand may represent an integer or a fraction.