Question

How do you write $2.9 \times {10^{10}}$ in standard form?

Answer 1

Hint: In order to write the given question $2.9 \times {10^{10}}$ into its standard form then , we need to multiply the $2.9$ by ${10^{10}}$ . And the multiplication of a decimal by tens, hundreds and thousands or etc. itself means that the decimal will be moved to the right side by as many as the number of zeroes are there in the multiplier. If suppose that the decimal number having less digits after the decimal than the multiplier ( or the number of zero is more ) , then the extra zeroes must be added to the final answer as it is . By following these steps we can find the desired result of writing decimal when multiplying and making it in standard form.

Complete step-by-step solution:
Let we have given a decimal number in the form $2.9 \times {10^{10}}$ where after decimal there is one digit . Here, in this question we have given decimal as $2.9$ .
So , to calculate the standard form of the given decimal , we have to first just do the multiplication of decimal value by ${10^{10}}$ and we get ,
 $2.9 \times {10^{10}}$

Now the decimal point moves one place to the right from $2.9$ to $29$ . But now the multiplier just used 2 zeroes to overcome the decimal and so we are left with ${10^9}$ as we know the fact that states If the decimal is being moved to the right, the exponent will be negative. That is now we have extra 9 zeros after moving decimal to right and the exponent becomes ${10^{10 - 1}} = {10^9}$ .

Now , as per the rule we are just simply going to put the zeroes to the product we got after moving the decimal . Then we are going to get ,
$29 \times {10^9}$
=$29000000000$
Hence, the result is $29000000000.0$ as we moved the decimal places 9 places to the right .

Note:
i) Do not Forget to verify the end of the result with the zeroes .
ii) If you multiply a decimal with 10 , then the decimal point will be moved to the right side by 1 place .
iii) If you multiply a decimal with 100 , then the decimal point will be moved to the right side by 2 place . iv) If you multiply a decimal with 1000 , then the decimal point will be moved to the right side by 3 place v) If the decimal number having less digits after the decimal than the multiplier ( or the number of zero is more ) , then the extra zeroes must be added to the final answer as it is .
vi) If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.