Question

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

Answer 1

=`6.125 xx 10^48`

Explanation:

To calculate: `3x^9 xx 5x^12`

multiply the numbers and add the indices `rArr 15x^21`

Do the same with `(2.5 xx 10^23) xx (2.45 xx 10^25)`

=`(2.5 xx 2.45) xx (10^23 xx 10^25)`

=`6.125 xx 10^48`

Answer 2

#(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 `axx10^n`, where `1<=a<10` and `n` is an integer and `1<=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 `(2.5xx10^23)xx(2.45xx10^25)`

= `(2.5xx2.45)xx(10^23xx10^25)`

= `(6.125)xx10^((23+25))`

= `6.125xx10^48`

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 `(2.5xx10^23)xx(2.45xx10^25)`

= `6,125,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000`