Question

The world population in 1995 was approximately 5.7 billion people. How do you write this number in standard form?

Answer 1

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.

We can thus solve this question by using the above stated definition of scientific notation.

Complete step by step solution:

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 \[5.7 \times {10^9}\].

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.