The exponent of the 10 of a number written in scientific notation tells you how many spaces you need to move the decimal of the number in order to convert it to standard notation. If the exponent is positive, move the decimal to the right and add 0s to fill in the place value digits. If the exponent is negative, move the decimal to the left and add 0s to fill in the place value digits.
Here I have some numbers that are already written in scientific notation and I’m asked to write the same numbers in standard notation. So what that involves is moving the decimal.
This first problem I’m going to start with 9.0 and then move the decimal 8 places to the left. Here we go. 1, 2, 3, 4, 5, 6, 7, 8, that’s where my new decimal goes and I’m going to fill in everything else with zeros. Zero point 1, 2, 3, 4, 5, 6, 7, zeros. So my answer looks like 0.00000009, that’s that number written in standard notation.
Same thing with this problem, I’m going to take 5.24 and move the decimal place 5 spots. But now I’m going to move it to the right so my number gets larger. 1, 2, 3, 4, 5, that’s where my new decimal is going to go, fill in with zeros and my answer is going to be 524,000 with three zeros behind it like that.
Moving from scientific notation into standard notation is pretty straight forward as long as you guys remember which way to move. The thing that I remember in my head is that 10 to the 5th is a really big number so I want to go from this small 5 value to something that’s really big. That helps me remember to move to the right as opposed to this 10 to the -8 is a really small number so I’m going to 9 and make it really small by moving the decimal point to the left. Maybe that’ll help you remember which way to move the decimals for scientific notation.
Experience the 'A-Ha!' moment with the best teachers
whom we hand-picked for you!
M.A. in Secondary Mathematics, Stanford University B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
“Your tutorials are good and you have a personality as well. I hope you have more advanced college level stuff, because I like the way you teach.”
“Thanks alot for such great lectures... I never found learning this easier ever before... keep up the great work.... :)”
“You seem so kind, it's awesome. Easier to learn from people who seem to be rooting for ya!' thanks”