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.

Important Questions on Powers

Learn and Prepare for any exam you want !

(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?

Important Questions on Powers

Learn and Prepare for any exam you want !