Video: Expressing a Number in Scientific Notation

Write 0.000853 in scientific notation.

02:05

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.

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