# How do you simplify and write (2.5times10^23)times (2.45times10^25) in standard notation?

Jul 1, 2016

=$6.125 \times {10}^{48}$

#### Explanation:

To calculate: $3 {x}^{9} \times 5 {x}^{12}$

multiply the numbers and add the indices $\Rightarrow 15 {x}^{21}$

Do the same with $\left(2.5 \times {10}^{23}\right) \times \left(2.45 \times {10}^{25}\right)$

=$\left(2.5 \times 2.45\right) \times \left({10}^{23} \times {10}^{25}\right)$

=$6.125 \times {10}^{48}$

Jul 1, 2016

(2.5xx10^23)xx(2.45xx10^25) =6,125,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

#### Explanation:

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of $10$. In other words, in scientific notation, a number is written as $a \times {10}^{n}$, where $1 \le a < 10$ and $n$ is an integer and $1 \le a < 10$.

To write the number in normal or standard notation one just needs to multiply by the power ${10}^{n}$ (or divide if $n$ is negative). This means moving decimal $n$ digits to right if multiplying by ${10}^{n}$ and moving decimal $n$ digits to left if dividing by ${10}^{n}$ (i.e. multiplying by ${10}^{- n}$).

In the given case, we have a multiplication of two numbers given in scientific notation. Hence, we first need to multiply the two numbers. Hence $\left(2.5 \times {10}^{23}\right) \times \left(2.45 \times {10}^{25}\right)$

= $\left(2.5 \times 2.45\right) \times \left({10}^{23} \times {10}^{25}\right)$

= $\left(6.125\right) \times {10}^{\left(23 + 25\right)}$

= $6.125 \times {10}^{48}$

Writing this number in standard form means, moving decimal digit to the right by $48$ points. But here we have three numbers to right of decimal, that means we have to add $45$ zeros after $5$ in $6.125$.

Hence in standard notation $\left(2.5 \times {10}^{23}\right) \times \left(2.45 \times {10}^{25}\right)$

= $6 , 125 , 000 , 000 , 000 , 000 , 000 , 000 , 000 , 000 , 000 , 000 , 000 , 000 , 000 , 000 , 000$