Question

What is $1.3 \times 10$ to the 0 power?

Answer 1

Hint: As we can see the question belongs to the zero power rule, as we know that any number that contains 0 as an exponent will be atlast equal to 1. And then we will go for the final solution.

Complete step by step answer:
As per the question, we can also write $1.3 \times 10$ to the 0 power as $1.3 \times {10^0}$. So, as we can see in the above term, 10 has its power as 0, which is something different. ${10^0}$ belongs to the Zero power rule or the rule for zero as exponent: Any nonzero real number raised to the power of zero is one, this means anything that looks like ${a^0}$​ will always equal 1 if a is not equal to zero.

Now, solve for the given term-
$1.3 \times {10^0} = 1.3 \times 1\,\,(\because {10^0} = 1) \\ $
$\therefore 1.3 \times {10^0} = 1.3$
In a nutshell, the multiplicative identity is 1, because \[1 \times x = x\] for every other number $x$ . Because any number to the zero power is simply the product of no numbers at all, which is the multiplicative identity, 1, any number to the zero power is one.0 to the power of anything else, on the other hand, is 0 because no matter how many times you multiply nothing by nothing, you get nothing.

Therefore, after solving for the given term $1.3 \times {10^0}$ , we get 1.3 as the final solution.

Note: In scientific notation, we write a number so that it has a single digit to the left of the decimal sign and is multiplied by an integer power of 10. In scientific notation, a number is written as $a \times {10^n}$ , where \[1 \leqslant a < 10\;\] and $n$ is an integer and \[1 \leqslant a < 10\;\]. Simply multiply by the power ${10^n}$ (or divide if n is negative) to write the number in normal or standard notation. When multiplying by ${10^n}$ , this implies moving decimal $n$ digits to the right, and when dividing by ${10^n}$ (i.e. multiplying by ${10^{ - n}}$ ), this means moving decimal $n$ digits to the left.
In the given case, as we have the number as $1.3 \times {10^0}$ we need not move the decimal digit to either side and hence in standard notation \[1.3 \times {10^0} = 1.3\] itself.