How do you write 3,610,000 in scientific form?

Question

Aurora Arias · Accepted Answer

#3.61xx10^6#

Take things one step at a time to understand what is going on.

The number is multiplied by ten to return it to its initial value of 3610000.

#color(blue)(3610000)# #color(blue)(361000).0xx10# #color(blue)(36100).00xx10xx10# #color(blue)(3610).000xx10xx10xx10# #color(blue)(361).0000xx10xx10xx10xx10# #color(blue)(36).10000xx10xx10xx10xx10xx10# #color(blue)(3).610000xx10xx10xx10xx10xx10xx10color(red)(larr" This one")#

Write as: #3.61xx10^6" "->" "#This has exactly the same value as #" "#3,610,000

Luna Angel · Answer

#3,610,000=3.61xx10^7# 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#. Note that moving decimal #p# digits to right is equivalent to multiplying by #10^p# and moving decimal #q# digits to left is equivalent to dividing by #10^q#. Hence, we should either divide the number by #10^p# i.e. multiply by #10^(-p)# (if moving decimal to right) or multiply the number by #10^q# (if moving decimal to left). In other words, it is written as #axx10^n#, where #1<=a<10# and #n# is an integer. To write #3,610,000# in scientific notation, we will have to move the decimal point six points to left, which literally means dividing by #10^7#. Hence in scientific notation #3,610,000=3.61xx10^7# (note that as we have moved decimal one point to right we are multiplying by #10^7# to compensate for division by #10^7#..

Aurora Arias · Answer

undefined 3,610,000 in scientific notation is $3.61 \times 10^6$.