Standard Notation to Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is written as a product of a number (between 1 and 10) and a power of 10.

To convert a large number to scientific notation, move the decimal point to the left until only one non-zero digit remains to the left of the decimal. Count the number of places you moved the decimal; this will be the positive exponent of 10.

4 x $$10^{10}$$ .

To convert a small number to scientific notation, move the decimal point to the right until only one non-zero digit remains to the left of the decimal. Count the number of places you moved the decimal; this will be the negative exponent of 10.

5 x $$10^{-4}$$ .

5.2 x $$10^{8}$$ .

3.7 x $$10^{-2}$$ .

2.203 x $$10^{-7}$$ .

The exponent in scientific notation indicates how many places the decimal point has been moved. A positive exponent means the original number is large, while a negative exponent means the original number is small.

To multiply numbers in scientific notation, multiply the coefficients and add the exponents of the powers of 10.