Scientific Notation is based on powers of the base number 10.

The number 123,000,000,000 in scientific notation is written as :

The second number is called the base . It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 10¹¹ the number 11 is referred to as the exponent or power of ten.

Rules for Division in Scientific Notation:

1) Divide the coefficients

2) Subtract the exponents (base 10 remains)

Example 1: (6 x 10⁶) / (2 x 10³) = 3 x 10³

What happens if the coefficient is less than 10?

Example 2: (2 x 10 ⁷) / (8 x 10³) = 0.25 x 10⁴

While the value is correct it is not correctly written in scientific notation since the coefficient is not between 1 and 10. We must move the decimal point over to the right until the coefficient is between 1 and 10. For each place we move the decimal over the exponent will be lowered 1 power of ten.

0.25x10 ⁴ = 2.5 x 10³ in scientific notation.

Now Try these:

(write your answers in the form of coefficientx10^exponent) If your answer is 3.5 x 10 ³ you should type 3.5x10^3 in the box then click the submit button).

What happens when the exponent(s) are negative?

We still subtract the exponents (apply the rules for subtracting signed numbers)

Example 5: (9 x 10 ^-6) / (3x 10^-3) = 3. x 10^-3

Example 6: (2 x 10 ³) / (4 x 10^-8) = 0.5 x 10¹¹ = 5 x 10 ¹⁰

Now Try these:

(write your answers in the form of coefficientx10^exponent) If your answer is 3.5 x 10 ³ you should type 3.5x10^3 in the box then click the submit button). Divide the following numbers using Scientific Notation.

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