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Algebra 1

5.6.5 Applying Scientific Notation

Algebra 15.6.5 Applying Scientific Notation

5.6.5 Applying Scientific Notation

5.6.5 • Applying Scientific Notation

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 7.5 × 10 3 7.5 × 10 3
Westcott Park 105,000
Brighton Park 4.5 × 10 2 4.5 × 10 2
Red Elk 22,300
Bear Park 1.1 × 10 5 1.1 × 10 5
Daniels Park 3,300
Blue Spruce 1.25 × 10 4 1.25 × 10 4
Yellow Jay Park 2.25 × 10 4 2.25 × 10 4

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 1.4 × 10 − 4 1.4 × 10 − 4
grain of pollen 0.00001014
one drop of water 0.00011
a feather 1.8 × 10 − 5 1.8 × 10 − 5
one kernel of corn 1.1 × 10 − 3 1.1 × 10 − 3
house fly 3.08 × 10 − 5 3.08 × 10 − 5

3. What do you notice when comparing numbers in scientific notation with different negative exponents?

Self Check

Which of the numbers shown is the greatest?
  1. 9.6 × 10 − 5
  2. 0.00084
  3. 7.2 × 10 − 3
  4. 0.0065

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 7.0 × 10 − 3 7.0 × 10 − 3
B 0.0000847
C 0.00022
D 1.8 × 10 − 4 1.8 × 10 − 4
E 8.92 × 10 − 3 8.92 × 10 − 3
F 6.03 × 10 − 2 6.03 × 10 − 2

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 7.0 × 10 − 3 = 0.007 7.0 × 10 − 3 = 0.007
B 0.0000847
C 0.00022
D 1.8 × 10 − 4 = 0.00018 1.8 × 10 − 4 = 0.00018
E 8.92 × 10 − 3 = 0.00892 8.92 × 10 − 3 = 0.00892
F 6.03 × 10 − 2 = 0.0603 6.03 × 10 − 2 = 0.0603

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 7.0 × 10 − 3 7.0 × 10 − 3
B 0.0000847 = 8.47 × 10 − 5 0.0000847 = 8.47 × 10 − 5
C 0.00022 = 2.2 × 10 − 4 0.00022 = 2.2 × 10 − 4
D 1.8 × 10 − 4 1.8 × 10 − 4
E 8.92 × 10 − 3 8.92 × 10 − 3
F 6.03 × 10 − 2 6.03 × 10 − 2

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

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 7.0 × 10 − 7 7.0 × 10 − 7
blue light 0.00000045
infrared light 5.0 × 10 − 4 5.0 × 10 − 4
ultraviolet light 2.0 × 10 − 9 2.0 × 10 − 9
microwaves 1.5 × 10 − 1 1.5 × 10 − 1
radio waves 2.1

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