Video: Converting Numbers into Scientific Notation

What is 0.00007 written in scientific notation?

02:22

Video Transcript

What is 0.00007 written in scientific notation?

A number is written in scientific notation if it is written in the form 𝑎 multiplied by 10 to the power of 𝑏, where the absolute value of 𝑎 must be less than 10 and greater than or equal to one and 𝑏 is a positive or negative integer. In this question, we want to write 0.00007 in scientific notation. Our first step is to find the first nonzero digit in our number. In this question, there is only one, the seven. We place a decimal point after this digit. Have there been other digits after this seven, we would’ve written these after the decimal point, for example, 7.124. In this case, there are no nonzero digits after the seven, so we have 7.0, or just seven.

We will multiply this by 10 raised to some power. Our value for 𝑏 will be negative for small numbers. This is because raising 10 to a negative power actually means we will be dividing. 10 to the power of negative four is the same as one over 10 to the power of four. So, we’re actually dividing by 10 to the power of four, which will make the number smaller.

To work out the value of 𝑏, we need to find the number of place values the numbers have moved or the number of times the decimal point has moved to the left. To get from 7.0 to 0.00007, we move our decimal point five places to the left. Therefore, our exponent is negative five. As 7.0 is the same as seven, 0.00007 written in scientific notation is seven multiplied by 10 to the power of negative five.

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