At the start of 2012, the population of the United States was approximately 313,269,000. What is this number written in scientific notation?

Question

Cameron Arnold · Accepted Answer

#3.13269000 xx10^8#

Given:#" "313269000#

The goal is to have one non-zero digit to the left of the decimal point. Since you altered the value, a mathematical correction must be made.

Multiply by 1 but in the form of #1=10^8/10^8# giving

#313269000xx10^8/10^8" "larr" this does not change the value"#

#313269000/10^8xx10^8#

#3.13269000 xx10^8" "larr" same value; just looks different!"#

The #10^8# is the mathematical correction which is in place but not applied.

Riley Anderson · Answer

#313269000=3.13269xx10^8# 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 #313269000# in scientific notation, we will have to move the decimal point eight point to the left, which literally means dividing by #10^8# for which we should compensate by multiplying it by #10^8#. Hence in scientific notation #313269000=3.13269xx10^8#.

Jeremiah Andrews · Answer

undefined The population of the United States in scientific notation is approximately $3.13269 \times 10^8$.