Video Transcript
Write 3.01 times 10 to the negative five in normal form.
To write a number in normal form is to just write it like we would normally write a number without any indices. For example, three million and 0.0076 are both numbers written in normal form. Therefore, the key to this question is to be able to interpret this number written in scientific form as a normal number. To do this, we must make careful note of the index of 10 here, which is negative five.
In particular, the fact that the index is negative means that this is a very small number rather than a very big number, since we are effectively dividing by 10 to the power of five. Now, in order to convert this to a normal number, one method is to consider its position in a decimal place value chart. Here, each column denotes a digit of a number, such as ones, tenths, hundredths, and so on. So 3.01 is written in the chart as follows.
So, how does 3.01 times 10 to the negative five fit into this chart? Well, if we multiply by 10 to the negative five, this is the same as dividing by 10 five times. So we shift the three digit five times to the right. So, the new number will have the three in the 10 to the negative five column. And for clarity, we can also fill the rest of the columns with zeros. Therefore, 3.01 times 10 to the negative five is 0.0000301 in normal form.
We note that this can be verified by observing that there are five zeros before the first nonzero digit, which coincides with the fact that the exponent is negative five. In summary, our final answer is 0.0000301.
