Method

Divide Numbers in Scientific Notation

Numbers written in scientific notation can be divided by using the properties of exponents. Use the Quotient of Powers Property to divide numbers written in scientific notation.

a* 10^b/c* 10^d = a/c * 10^(b-d)

Consider the division of the following two numbers. 0.36 * 10^(23)/1200 These numbers written in scientific notation, and they can be divided in four steps. It is similar to the process of multiplying numbers written in scientific notation.

Write Each Number in Scientific Notation

Start by checking whether each number is written in scientific notation. c First Factor & * & Second Factor 0.36 & * & 10^(23) & * The first factor is less than 1. That means the dividend still needs to be written in scientific notation. Move the decimal point to the right until 0.36 is greater than 1 and less than 10. Then, decrease the second factor's exponent by the number of moves. 0.36 * 10^(23) ⇔ 3.6 * 10^(22) Next, consider the divisor. The divisor 1200 is a whole number. Note that 1200 can also be expressed as 1200.0. Now, move the decimal point three units to the left to get a first factor that is less than 10 and greater than 1. The second factor can then be written as 10 to the power of 3. 1200 ⇔ 1.2 * 10^3

Divide the First Factors

Now that both the dividend and divisor are written in scientific notation, the first factors of both can be divided.

3.6 * 10^(22)/1.2 * 10^3

WriteProdFrac

Write as a product of fractions

3.6/1.2 * 10^(22)/10^3

CalcQuot

Calculate quotient

3 * 10^(22)/10^3

Divide the Second Factors

Next, use the Quotient of Powers Property to divide the second factors. This property states that when dividing powers with the same base, the exponents are subtracted.

3 * 10^(22)/10^3

DivPow

a^m/a^n= a^(m-n)

3 * 10^(19)

Write the Result in Scientific Notation

Finally, write the resulting number in scientific notation. Notice that in this instance, the quotient is already in scientific notation. 3 * 10^(19)

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