Indices

Index of a Rational Number

The distance between the sun and Earth is approximately 148800000000 m. The speed of light is 300000000 m/s. Now, can you calculate the time taken by light to reach Earth from the sun?

Since light travels at a speed of 300000000 m/s, it travels 300000000 metres in 1 second. Therefore, to calculate the time required by light to reach Earth from the sun, we have to divide the distance between the sun and Earth by the speed of light.

∴ Time taken by light to reach Earth from sun

This calculation involved two very large numbers. In such cases, we might make mistakes while writing the numbers. If we mistakenly add or subtract even one 0 from any of the numbers, then it will drastically affect our answer.

For example, the speed of light has eight 0s after the digit 3. By mistake, if we write seven 0s after the digit 3, then let us see what the answer will be.

Time taken by light to reach Earth from sun

Now, note the difference between the two answers i.e., 8.3 minutes and 83 minutes. In order to avoid these mistakes, it is best to first convert such large numbers into their standard forms.

The rule to write a number in its standard form is