Unit 7, Lesson 11
Representing Small Numbers on the Number Line
Grade 8
11.1
Warm-up
Kiran drew this number line.
A number line, 11 tick marks, 0, 1 times 10 to the negative 4 power, 2 times 10 to the negative 4 power, 3 times 10 to the negative 4 power, 4 times 10 to the negative 4 power, 5 times 10 to the negative 4 power, 6 times 10 to the negative 4 power, 7 times 10 to the negative 4 power, 8 times 10 to the negative 4 power, 9 times 10 to the negative 4 power, 10 to the negative 5 power.
Andre said, “That doesn’t look right to me.”
Explain why Kiran is correct or explain how he can fix the number line.
11.2
Activity
-
Label the tick marks on the number line.
-
Plot the following numbers on the number line:
A.
B.
C.
D.
- Which is larger, or ? Estimate how many times larger.
- Which is larger, or ? Estimate how many times larger.
11.3
Activity
- The radius of an electron is about 0.0000000000003 cm.
- Write this number as a multiple of a power of 10.
-
Decide what power of 10 to put on the right side of this number line and label it.
-
Label each tick mark as a multiple of a power of 10.
-
Plot the radius of the electron in centimeters on the number line.
- The mass of a proton is about 0.0000000000000000000000017 grams.
- Write this number as a multiple of a power of 10.
-
Decide what power of 10 to put on the right side of this number line and label it.
-
Label each tick mark as a multiple of a power of 10.
-
Plot the mass of the proton in grams on the number line.
-
Point on the zoomed-in number line describes the wavelength of a certain X-ray in meters.
A number line, 11 tick marks, 0, 1 times 10 to the negative 12 power, 2 times 10 to the negative 12 power, 3 times 10 to the negative 12 power, 4 times 10 to the negative 12 power, 5 times 10 to the negative 12 power, 6 times 10 to the negative 12 power, 7 times 10 to the negative 12 power, 8 times 10 to the negative 12 power, 9 times 10 to the negative 12 power, 10 to the negative 11 power. Six times 10 to the negative 12 power to 7 times 10 to the negative 12 power is zoomed out to a new number line with 11 tick marks. The second is labeled A.- Write the wavelength of the X-ray as a multiple of a power of 10.
- Write the wavelength of the X-ray as a decimal.
Student Lesson Summary
The width of a bacterium cell is about meters. If we want to plot this on a number line, we need to find which two powers of 10 it lies between. We can see that is a multiple of . So our number line will be labeled with multiples of .
A number line, 11 tick marks, 0, 1 times 10 to the power negative 6, 2 times 10 to the power negative 6, 3 times 10 to the power negative 6, 4 times 10 to the power negative 6, 5 times 10 to the power negative 6, 6 times 10 to the power negative 6, 7 times 10 to the power negative 6, 8 times 10 to the power negative 6, 9 times 10 to the power negative 6, 10 the power negative 5.
Note that the right side is labeled because .
The power of 10 on the right side of the number line is always greater than the power on the left. This is true for powers with positive or negative exponents.
None