Move the decimal until the resulting number is greater than 1 and less than 10. The number of places the decimal moves is the exponent of 10 in scientific notation.
B
Move the decimal until the resulting number is greater than 1 and less than 10. The number of places the decimal moves is the exponent of 10 in scientific notation.
C
Move the decimal until the resulting number is greater than 1 and less than 10. The number of places the decimal moves is the exponent of 10 in scientific notation.
A
5.4678* 10^3
B
3.2 * 10^(- 3)
C
8.00702 * 10^6
Practice makes perfect
A number written in scientific notation usually expresses a very large or very small number by writing its value as the product of the number's first nonzero digit and 10 to some power. Let's look at some examples.
Standard Notation
Scientific Notation
5 0 000 000 000
5 * 10^(10)
5 00 000
5 * 10^5
5 0
5 * 10^1
5
5 * 10^0
0.5
5 * 10^(- 1)
0.00005
5 * 10^(- 5)
0.0000000005
5 * 10^(- 10)
To change from standard form to scientific notation, we need to move the decimal until the resulting number is greater than 1 and less than 10. The number of places the decimal moves is the exponent of 10. Let's take a look at the given number.
5 467.8
This number is greater than 10, so the decimal point will move to the left. The decimal must move three places, which will be the power of 10.
This means that the scientific notation of 5467.8 is 5.4678 * 10^3.
Standard Form:& 5467.8 Scientific Notation:& 5.4678 * 10^3
Let's consider the given number.
0.0032
Notice that this number is less than 10. As such, the decimal point will move to the right. The decimal must move three places before passing the first nonzero digit, so this is the power of 10.
This means that the scientific notation of 0.0032 is 3.2 * 10^(- 3).
Standard Form:& 0.0032 Scientific Notation:& 3.2* 10^(- 3)
We are given the following number.
8 007 020
This number is greater than 10, so the decimal point will move to the left. The decimal must move six places, which will be the power of 10.
This means that the scientific notation of 8 007 020 is 8.00702 * 10^6.
Standard Form:& 8 007 020 Scientific Notation:& 8.00702* 10^6
