Question

How do you write $7.2\times {{10}^{5}}$ in standard form?

Answer 1

Hint: Now we want to write the number in standard form. To do so we will first write the power of 10 and shift the decimal accordingly. Since here the power is positive 5 we will shift the decimal to right by 5 places and hence get the required number.

Complete step-by-step solution:
Now we know that we can add zero to the right of decimal without changing its value. Hence 7.2 is the same as 7.200000.
Now we are multiplying the number by power of 10.
Now let's see what happens when we multiply the number by a power of 10.
If the index is positive then we shift the decimal to right. Similarly if the index is negative then we shift the decimal to left.
Hence if we multiply a decimal by ${{10}^{3}}$ then we will shift the decimal to right by 5 places.
Similarly if we multiply the number by ${{10}^{-3}}$ then we will shift the decimal to left by 3 places.
Now consider the given number $7.2\times {{10}^{5}}$
We can write this number as $7.20000\times {{10}^{5}}$
Now shifting the decimal to right by 5 places we get, 720000.
Hence the given number is nothing but 720,000.

Note: Now note that if an integer is multiplied with a power of 10 then we simply add the number of zeroes equal to the index given. For example if we have $5\times {{10}^{3}}$ then we will add 3 zeros to 5 and hence obtain the number as $5000$.