Scientific notation is a way of writing numbers that are too big or too small to be conveniently written in decimal form.
Quick Tutorial and Practice Questions
Science notation is a very simple and effective way of representing very large numbers in simpler forms. For example, instead of writing out 149,600,000,000 meters, which is the estimated distance from the sun, astronomers could easily write it out as 1.496 x 1011 meters. Scientific notation expresses numbers in their powers of ten.
It can also be used to express simple numbers. For example, using scientific notation, 10 = 101 The exponent “1” tell the number of times to multiply by 10 to get the original number.
100 = 102
1000 = 10³
10⁰ = 1
When the exponent is negative, it tells us how many times we need to divide by ten to get the original number.
For example, 0.025 = 2.5 x 10
The accepted format of scientific notation or writing numbers on their powers of 10 is a x 10n Where ‘a’ must be between 1 and 10, and n must be an integer.
To convert a number to scientific notation, place a decimal after the first number that is not a zero, or, after the first number that between 1 and 9.
After placing the decimal, count the number of places the decimal had to move to get the exponent of 10. If the decimal moves to the left, then the exponent to multiply 10 will be in the positive. If the decimal moves from right to left, it will be a negative power of 10.
For example, to convert 29010, we need to place a decimal
after 2, since 2 is the first non zero number. We
would then have 2.91
If we were to convert 0.0167, we need to place the decimal after 1, since the first two numbers before 1 are zeros, and do not fall between 1 and 9. We would thus have 1.67
To complete the conversion of 29010 to scientific notation,
we would get 2.91 x 10⁴
The 10 is raised to the power of 4, because there are 4 places counting from right to left. This scientific notation is positive because the decimal moved to the left.
0.0167 = 1.67 x 10-2
In this example, the decimal place moved from left to right by 2 spaces thus the 10 is raised to the power of 2. It is negative, because the decimal moved to the right.
How to convert from scientific notation
You may also need to convert numbers that are already represented in scientific notation or in their power of ten, to regular numbers.
First it is important to remember these two laws.
If the power is positive, shift decimal to the right
If the power is negative, shift decimal point to the left
1. Convert 7,892,000,000 to scientific notation.
A. 7.892 x 1010
B. 7.892 x 10-9
C. 7.892 x 109
D. 0.7892 x 1011
2. Convert 0.045 to scientific notation.
A. 4.5 x 10-2
B. 4.5 x 102
C. 4.05 x 10-2
D. 4.5 x 10-3
3. Convert 204 to scientific notation.
A. 2.04 x 10-2
B. 0.204 x 102
C. 2.04 x 103
D. 2.04 x 102
4. Convert 0.00002011 to scientific notation.
A. 2.011 x 10-4
B. 2.011 x 105
C. 2.011 x 10-6
D. 2.011 x 10-5
5. Convert this scientific notation back to its original number: 2.63 x 10-2
6. Convert this scientific notation back to its original number: 5.63 x 106
The decimal point moves 9 spaces right to be placed after 7, which is the first non-zero number. Thus 7.892 x 109
The decimal point moves 2 spaces to the left to be placed before 4, which is the first non-zero number. Thus its 4.5 x 10-2 The answer is in negative since the decimal moved left.
The decimal point moves 2 spaces right to be placed after 2, which is the first non-zero number. Thus it is 2.04 x 102
The decimal point moves 5 places left to be placed after 2, which is the first non-zero number. Thus its 2.011 x 10-5 The answer is in the negative because the decimal moved left.
The scientific notation is in the negative so we shift the decimal 2 places to the left. Thus its 0.0263.
The scientific notation is in the positive so we shift the decimal 6 places to the right. Thus it is 5,630,000.
Modified: August 26th, 2018 August 26th, 2018
Published: April 6th, 2014