
The world population in 1995 was approximately 5.7 billion people. How do you write this number in standard form?
Answer
552k+ views
Hint: We can write the given number in standard form using the concept of scientific notation. Scientific notation of a number is the representation of numbers in such a way that very large numbers can be read easily without any discrepancy. Also in scientific notation the numbers are represented in the form $p \times {10^n}$ where $p$ should be between 1 and 10 i.e. \[1 \leqslant p < 10\] and $n$ is an integer.
Complete step by step solution:
Note: To convert a number to scientific notation, certain rules have to be followed such as the position of the decimal point should be such that there is only a single digit before it. Also while moving the decimal points one should take care about the position which has been moved since it determines the power of 10.
We can thus solve this question by using the above stated definition of scientific notation.
Given statement:
World population in 1995: $5.7\;{\text{billion}}\;{\text{people}}....................................\left( i \right)$
We also know that \[1{\text{ billion: }}1,000,000,000\]
So substituting it in (i) we can write:
World population in 1995: $5,700,000,000....................................\left( {ii} \right)$
Now we know that the basic definition of scientific notation the numbers are represented in the form $p \times {10^n}$ where $1 \leqslant p < 10$ and $n$ is an integer.
Such that we have to find $p\;{\text{and}}\;n$ for the number $5,700,000,000$.
Now in order to find $p$ we have to move the position of decimal such that there is only a single digit before it.
So we get:
$ \Rightarrow 5,700,000,000 = 5.700000000................\left( {iii} \right)$
So we can write $p = 5.7$
Now in order to find $n$ we have to determine the position of decimal which has been moved:
So here since it has been moved to the left side by $9$ positions, we can write:
$n = {10^9}........................\left( {iv} \right)$
If it had been in the right direction then the sign would be negative.
So from (iii) and (iv) we can write:
\[\Rightarrow p \times {10^n} = 5.7 \times {10^9}\]
\[\Rightarrow 5,700,000,000 = 5.7 \times {10^9}..........\left( v \right) \]
Therefore the population \[5,700,000,000\] in standard form will be \[5.7 \times {10^9}\].
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