Activity
1. How would you write each of the following numbers in scientific notation?
Decimal Form | Scientific Notation |
0.00000654 | |
0.0000947 | |
683,000 | |
0.022 | |
5,200 | |
0.000352 |
Compare your answers:
Decimal Form | Scientific Notation |
0.00000654 | |
0.0000947 | |
683,000 | |
0.022 | |
5,200 | |
0.000352 |
2. How would you write each of the following scientific notation values in decimal form?
Scientific Notation | Decimal Form |
Compare your answers:
Scientific Notation | Decimal Form |
0.000726 | |
0.0332 | |
9,400,000 | |
0.887 | |
63,950 | |
0.004 |
Video: Converting between Scientific Notation and Decimal Form
Watch the following video to learn more about rewriting scientific notation in decimal form and decimal form in scientific notation.
Self Check
Additional Resources
Using Scientific Notation
Working with very large or very small numbers can be awkward. Since our number system is base ten, we can use powers of ten to rewrite very large or very small numbers to make them easier to work with. Consider the numbers 4,000 and 0.004.
Using place value, we can rewrite the numbers 4,000 and 0.004. We know that 4,000 means and 0.004 means .
If we write the 1,000 as a power of ten in exponential form, we can rewrite these numbers in this way:
4,000
0.004
When a number is written as a product of two numbers, where the first factor is a number greater than or equal to 1 but less than 10, and the second factor is a power of 10 written in exponential form, it is said to be in scientific notation.
A number is expressed in scientific notation when it is in this form :
, where and is an integer.
It is customary in scientific notation to use × as the multiplication sign, even though we avoid using this sign elsewhere in algebra.
To convert a decimal to scientific notation:
Step 1. Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.
Step 2. Count the number of decimal places, , that the decimal point was moved.
Step 3. Write the number as a product with a power of 10. If the original number is
- greater than 1, the power of 10 will be .
- between 0 and 1, the power of 10 will be .
Step 4. Check.
Example
Write in scientific notation:
- 37,000
Solution
0.0052
Solution
To convert scientific notation to decimal form:
Step 1. Determine the exponent, , on the factor of 10.
Step 2. Move the decimal places, adding zeros if needed.
- If the exponent is positive, move the decimal point places to the right.
- If the exponent is negative, move the decimal point places to the left.
Step 3. Check.
Example
Write in decimal form:
Solution
Solution
Try it
Try It: Using Scientific Notation
Write in scientific notation.
1. 65,000,000
2. 0.00034
Write in decimal form.
3.
4.
Compare your answers:
Here is how to write the numbers:
- 530,000
- 0.00425