How do you convert #3.5 * 10^4# to standard form?

Question

Noah Archer · Accepted Answer

#3.5xx10 = 35#
#3.5xx10^2=350#
#3.5xx10^3=3500#
#3.5xx10^4=35000# ,~~~~~~~~~~#color(blue)(" Explaining what is happening ")#~~~~~~~~~~~~~~~~~ Consider the value #3.5# we are saying that we are counting in units (1's) in that we have #3 1/2" of 1's"# '.....................................................................................
Consider the value #3.5xx10#. Now we are saying we have #3 1/2# of tens. That is; 3 lots of 10 is 30 and #1/2# of 10 is 5 so we have #30+5=35#
'................................................................................. Note that #10^2# is 100
Consider the value #3.5xx10^2#. Now we are saying we have #3 1/2" of "100's# #color(brown)("So if we are counting in 100's then the decimal point stays where")##color(brown)("it is and we move the number of 3.5 to the left until the")##color(brown)("3 becomes hundreds.")# Note that we have to insert a place holder of 0 just to the left of the decimal point to make sure the three is viewed as in the hundreds. #color(brown)(3.5xx10^2) color(blue)(" "vec("slide to the left 2 places")" "350.0#
#"                                                                "color(green)(uarr)#
#"                                                    "color(green)("Place keeper of 0")#

Genesis Amaya · Answer

In standard notation #3.5xx10^4=35000# 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, as we have the number as #3.5xx10^4#, we need to move decimal digit to the right by three points. For this, let us write #3.5# as #3.50000# and moving decimal point four points to right means #35000.0# Hence in standard notation #3.5xx10^4=35000#