The first factor is already less than 10 and greater than 1.
C
The second factor should be written as a power of 10.
D
The first factor should be greater than or equal to 1.
A
9.25* 10^(- 1)
B
The number is already in scientific notation.
C
2.8* 10^1
D
8.3* 10^3
Practice makes perfect
We want to determine whether the number is written in the scientific notation.
92.5* 10^(- 2)
A number in scientific notation is the product of two factors. The first factor is a number less than 10 and greater than or equal to 1. The second factor is some power of 10. Let's look at some examples.
Scientific Notation
Standard Notation
5 * 10^(10)
5 0 000 000 000
5 * 10^5
5 00 000
5 * 10^1
5 0
5 * 10^0
5
5 * 10^(- 1)
0.5
5 * 10^(- 5)
0.00005
5 * 10^(- 10)
0.0000000005
The first factor in 92.5* 10^(- 2), 92.5, is greater than 10. Therefore, this number is not scientific notation. We should move the decimal point one place to the left. The number of places the decimal moves to the left is added to the exponent of 10.
92.5* 10^(- 2) = 9.25 * 10^(- 2 + 1)
The scientific form of the number is 9.25 * 10^(- 1).
A number in scientific form is the product of two factors. The first factor is a number less than 10 and greater than or equal to 1. The second factor is a power of 10. Let's consider the given number.
6.875* 10^2
We can see that this number satisfies all conditions, so it is written in scientific form.
A number in scientific form is the product of two factors. The first factor is a number less than 10 and greater than or equal to 1. The second factor is a power of 10. Let's consider the given number.
2.8* 10
We can see that 2.8 is greater than 1 and less than 10. The second factor is not in the correct form. We need to rewrite it as a power of 10. Since 10 is equal to 10^1, we can write the number in scientific notation.
2.8* 10 = 2.8 * 10^1
A number in scientific form is the product of two factors. The first factor is a number less than 10 and greater than or equal to 1. The second factor is a power of 10. Let's consider the given number.
0.83* 100^2
Here, both factors are in the incorrect form. Let's start by rewriting 100^2. We know that 100^2 is the product 100* 100. Let's find it!
100* 100 = 10 000
To write 10 000 as a power of 10, we count the number of zeros and write it as an exponent of 10.
1 0 000 = 10^4
Let's use this to rewrite the original form of the number.
0.83* 100^2 = 0.83 * 10^4
Now let's change the form of the first number. Note that 0.83 is less than 1. The first factor should be greater than or equal to 1. Let's move the decimal point one place to the right. The number of places the decimal moves to the left is added to the exponent of 10. Here, we move the decimal point to the right, so we will subtract the number of digits we move the decimal place.
0.83* 10^4 = 8.3 * 10^(4 - 1)
The scientific form of the number is 8.3 * 10^3.
