Question

Select the PROPER Scientific Notation for the following value. 659,000,000,000 Question 1 options: 659 × 109 65.9 × 1010 6.59 × 1011 0.659 × 1012

Answer 1

The proper notation may depend on where you are. In the US, we like there to be one non-zero digit to the left of the decimal point, hence the appropriate form is ...

... 6.59×10¹¹

_____

Elsewhere, the "proper" form may require the first non-zero digit be placed to the right of the decimal point, as in 0.659×10¹². This is also the form used by some computer languages.

In Engineering usage, quite often the desired form is one that has the exponent be a multiple of 3, so the appropriate forms would be 659×10⁹ or 0.659×10¹².

Sometimes when you're doing problems using numbers in scientific notation, it can be convenient to scale the operands so the result comes out with no need for rescaling. For example, if you were to divide 100 by this number, you might write ...

... 100/(65.9×10¹⁰) ≈ 1.517×10⁻¹⁰

Without this "pre-scaling", you would get

... (10²)/(6.59×10¹¹) ≈ 0.1517×10⁻⁹ = 1.517×10⁻¹⁰

which requires rescaling the answer.