Very large or very small numbers are sometimes written in scientific notation. A number written in scientific notation is a decimal number between 1 and 10 multiplied by a power of 10.
Example 1
Express the following in scientific notation.
2,100,000 written in scientific notation is 2.1 × 10 6. Simply place the decimal point to get a number between 1 and 10 and then count the digits to the right of the decimal to get the power of 10.
0.0000004 written in scientific notation is 4.0 × 10 –7. Simply place the decimal point to get a number between 1 and 10 and then count the digits from the original decimal point to the new one.
Notice that number values greater than 1 have positive exponents as the power of 10 and that number values between 0 and 1 have negative exponents as the power of 10.
Multiplication in scientific notation
To multiply numbers in scientific notation, multiply the numbers that are between 1 and 10 together to get a whole number. Then add the exponents on the 10's to get a new exponent on 10. It may be necessary to make adjustments to this answer in order to correctly express it in scientific notation.
Example 2
Multiply and express the answers in scientific notation.
This answer must be changed to scientific notation (first number from 1 to 9):
30 × 10 12 = 3.0 × 10 1 × 10 12 = 3.0 × 10 13
c
Division in scientific notation
To divide numbers in scientific notation, divide the numbers that are between 1 and 10 to get a decimal number. Then subtract the exponents on the 10s to get a new exponent on 10. It may be necessary to make adjustments to this answer in order to correctly express it in scientific notation.
Example 3
Divide and express the answers in scientific notation.
This answer must be changed to scientific notation.
0.4 × 10 2 = 4 × 10 –1 × 10 2 = 4 × 10 1
e
FAQs
Numbers in scientific notation are written with three parts. A coefficient, a base, and a power. For example, 3.5×104 has a coefficient of 3.5, a base of 10, and a power of 4. The power of 4 indicates that 3.5 should be multiplied by 104, which is 35,000.
What are 5 examples of scientific notation? ›
| 10000 = 1 x 104 | 24327 = 2.4327 x 104 |
|---|
| 1 = 100 | |
| 1/10 = 0.1 = 1 x 10-1 | 0.32 = 3.2 x 10-1 (not usually done) |
| 1/100 = 0.01 = 1 x 10-2 | 0.053 = 5.3 x 10-2 |
| 1/1000 = 0.001 = 1 x 10-3 | 0.0078 = 7.8 x 10-3 |
4 more rows2x10^5 to one significant figure. If any of the zeros in your original number were significant then include them. E.g. 3 of the zeros were significant, then write: 2.000x10^5.
How to multiply scientific notation? ›
Multiplication: To multiply numbers in scientific notation, multiply the decimal numbers. Then add the exponents of the powers of 10. Place the new power of 10 with the decimal in scientific notation form.
How to read scientific notation e? ›
The Scientific format displays a number in exponential notation, replacing part of the number with E+n, in which E (exponent) multiplies the preceding number by 10 to the nth power. For example, a 2-decimal scientific format displays 12345678901 as 1.23E+10, which is 1.23 times 10 to the 10th power.
How do you write 2000000000000 in scientific notation? ›
Every number can be expressed in Scientific Notation. In our first example, 200,000,000,000 should be written as 2.0 x 1011. In theory, it can be written as 20 x 1010, but by convention the number is usually written as 2.0 x 1011 so that the lead number is less than 10, followed by as many decimal places as necessary.
How do you write 1000000000 in scientific notation? ›
Scientific notation is essentially moving the decimal point from the end of the number to just before the first non-zero number. The number is then shown to be multiplied by an exponent of ten that accomplishes this manipulation. So, the scientific notation for 1,000,000,000 is 1 x 10 9.
What is 7000 000 000 in scientific notation? ›
\[7,000,000,000\] can be rewritten as $7 \times 1000000000$ . Hence the scientific notation of $7,000,000,000$ is $7 \times {10^9}$ .
Can scientific notation be more than 10? ›
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
What does e mean in math? ›
Euler's Number 'e' is a numerical constant used in mathematical calculations. The value of e is 2.718281828459045…so on. Just like pi(π), e is also an irrational number. It is described basically under logarithm concepts.
College Algebra Tutorial 3
- Step 1: Move the decimal point so that you have a number that is between 1 and 10. ...
- Step 2: Count the number of decimal places moved in Step 1 . ...
- Step 3: Write as a product of the number (found in Step 1) and 10 raised to the power of the count (found in Step 2).
