Activity
1. A biologist receives bird population estimates for different parks. The estimates are shown in the table. Work with your partner to arrange these estimates in order from least to greatest.
Park | Bird Population |
Shady Elm | |
Westcott Park | 105,000 |
Brighton Park | |
Red Elk | 22,300 |
Bear Park | |
Daniels Park | 3,300 |
Blue Spruce | |
Yellow Jay Park |
Compare your answer:
- Brighton Park,
- Daniels Park, 3,300
- Shady Elm,
- Blue Spruce,
- Red Elk, 22,300
- Yellow Jay Park,
- Westcott Park, 105,000
- Bear Park,
2. Enrico weighs the small objects shown for a science project. Work with your partner to arrange these weights in order from heaviest to lightest.
Object | Weight (lb) |
grain of sand | |
grain of pollen | 0.00001014 |
one drop of water | 0.00011 |
a feather | |
one kernel of corn | |
house fly |
Compare your answer:
- one kernel of corn,
- grain of sand,
- one drop of water, 0.00011
- house fly,
- a feather,
- grain of pollen, 0.00001014
3. What do you notice when comparing numbers in scientific notation with different negative exponents?
Compare your answer:
If both exponents are negative, then the number with the smaller absolute value exponent is the larger number. For example, the number with the exponent is larger than the number with the exponent .
Self Check
Additional Resources
Applying Scientific Notation
Let’s look at how to solve a real-world problem involving scientific notation.
The specimens below are measured lengths of different tiny animals. Arrange them in order from shortest to longest.
Specimen | Length (m) |
A | |
B | 0.0000847 |
C | 0.00022 |
D | |
E | |
F |
To solve this problem, we can convert all of the measurements to decimal form or standard form.
Let’s convert all measurements to decimal form from scientific notation.
Specimen | Length (m) |
A | |
B | 0.0000847 |
C | 0.00022 |
D | |
E | |
F |
We can now arrange the decimal values in order from shortest to longest:
B, D, C, A, E, F
Let’s convert each length into scientific notation and check our answer.
Specimen | Length (m) |
A | |
B | |
C | |
D | |
E | |
F |
The negative exponent with the largest absolute value represents the smallest number, so B is the shortest length.
The negative exponent with the smallest absolute value represents the largest number, so F is the longest length.
When the exponents are equal, compare the decimal part of the number.
The order B, D, C, A, E, F is correct from shortest to longest length.
Try it
Try It: Applying Scientific Notation
The measurements in the table are sample wavelengths for the given types of waves. Arrange them in order from shortest to longest.
Color | Wavelength (m) |
red light | |
blue light | 0.00000045 |
infrared light | |
ultraviolet light | |
microwaves | |
radio waves | 2.1 |
Compare your answers:
Here is how to arrange the measurements from shortest to longest:
Let’s convert the values for blue light and radio waves into scientific notation to compare all the values.
blue light =
radio waves =
So, from shortest to longest the wavelengths are:
- ultraviolet light,
- blue light,
- red light,
- infrared light,
- microwaves,
- radio waves,