# Is the number 12.38 X 10^2 in scientific notation and how do you know?

Mar 25, 2015

Technically $12.38 \times {10}^{2}$ is in scientific notation ; any number expressed in the form $a \times {10}^{b}$ is in scientific notation.

However, it is not in normalized scientific notation . In normalized scientific notation, there is exactly 1 non-zero digit to the left of the decimal point in the $a$ term (with an exception being made for zero which in scientific notation is written as $0.0 \times {10}^{1}$).

In normalized scientific notation, your original value would be written as $1.238 \times {10}^{3}$

Mar 25, 2015

It's not in correct scientic notation.

The correct notation should be $1.238 \cdot {10}^{3}$

The rule is that the number before the $10$power must be from $1$ up to (but not including) $10$, so you allways have just one (non-zero) digit before the decimal point.

The exception is when you have a table of values. In that case you use the same $10$power throughout (example: a table of specific masses for different materials).