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

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#

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#