Name: Expressing Large Numbers in Standard Form
Uploaded: 2019-07-19
Duration: 7 min 22 s
Description: Any number can be expressed as decimal numbers between 1 and 10 multiplied by a power of 10. In this video, we will learn about expressing large numbers in standard form.

Question

(i) The distance between Sun and Saturn is $1433500000000 m$ .

(ii) The distance between Saturn and Uranus is $1439000000000 m$ .

(iii) The distance between Sun and Earth is $149600000000 m$ .

Represent the above distances in scientific notation and then find out which of these three distances is maximum?

Accepted Answer

We know that,

A number in scientific notation is given as the product of a number (integer or decimal) and a power of $10$ . We move the decimal place forward or backward until we have a number between $1 and 10 .$ Then we add a power of ten that tells how many places you moved the decimal forward or backward.

The scientific notation is given by $c \times 10^{n}$ .

$\begin{array}{rcl} 1433500000000 & = & 14335 \times 10^{8} \end{array}$

$= 1.4335 \times 10^{4} \times 10^{8} (∵ a^{m} \times a^{n} = a^{m + n})$

$\begin{array}{rcl} = \end{array} \begin{array}{rcl} 1 \end{array} \begin{array}{rcl} . \end{array} \begin{array}{rcl} 4335 \end{array} \begin{array}{rcl} \times \end{array} \begin{array}{rcl} 10^{12} \end{array}$

$\begin{array}{rcl} 1439000000000 \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} 1439 \end{array} \begin{array}{rcl} \times \end{array} \begin{array}{rcl} 10^{9} \end{array}$

$= 1.439 \times 10^{3} \times 10^{9} (∵ a^{m} \times a^{n} = a^{m + n})$

$= 1.439 \times 10^{12}$

$\begin{array}{rcl} 149600000000 \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} 1496 \end{array} \begin{array}{rcl} \times \end{array} \begin{array}{rcl} 10^{8} \end{array}$

$= 1.496 \times 10^{3} \times 10^{8} (∵ a^{m} \times a^{n} = a^{m + n})$

$= 1.496 \times 10^{11}$

Now, let us compare the numbers,

$1.439 \times 10^{12} > 1.4335 \times 10^{12} > 1.496 \times 10^{11}$

Hence, $\begin{array}{rcl} 1439000000000 \end{array}$ is the maximum distance.

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