How do you write #297.1# in scientific notation?

Question

Cameron Arnold · Accepted Answer

#297.1=2.971xx10^2# 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 #297.1# in scientific notation, we will have to move the decimal point two points to left, which literally means dividing by #10^2#. Hence, we have to multiply by #10^2# too along with shifting decimal point. Hence in scientific notation #297.1=2.971xx10^2#.

Everly Taylor · Answer

#2.971xx10^2#

The objective is to have #color(brown)("just one non zero digit to the left of the ")##color(brown)("decimal point")#. In doing this we change the value so we have to include a #color(magenta)("mathematical correction")# that, if it were to be applied, would return the new value back to the original number.

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Multiply by 1 but in the form of #1=100/100#

#297.1xx100/100#

Multiplying by 1 in the form of #100/100# does not change the value but it does change the way it looks.

#297.1/100xx100#

#2.971xx100#

#2.971xx10^2#

Skylar Adams · Answer

undefined To write 297.1 in scientific notation, it would be expressed as $2.971 \times 10^2$.