### Video Transcript

Write 0.000853 in scientific notation.

A number is written in scientific
notation when it is in the form 𝑎 multiplied by 10 to the power of 𝑏. We know that the absolute value of
𝑎 must be less than 10 and greater than or equal to one. We know that 𝑏 must be an
integer. It is a positive integer for large
numbers and a negative integer for small numbers. In this question, we want to write
the small number 0.000853 in scientific notation. We begin by finding the first
nonzero digit, in this case, eight. We put a decimal point after this
number and then write any further nonzero digits. In this question, our value of 𝑎
is 8.53. This is less than 10 and greater
than or equal to one.

We need to multiply this by 10
raised to some power. In this case, the power or exponent
will be negative as to get from 8.53 to 0.000853, we are actually dividing. Multiplying by 10 to the power of
negative six is the same as dividing by 10 to the power of six. To work out the value of this
exponent, we need to work out how many places our digits have moved, or how many
times the decimal point has moved. In this case, it is four. Therefore, our exponent is negative
four. The number 0.000853 written in
scientific notation is 8.53 multiplied by 10 to the power of negative four.