1. Negative Exponents

2. Unit of Measure
Standard Form (m)
Exponential Form
Gigametre
109
Megametre
106
Kilometre
1 000
103
Hectometre
100
102
Decametre 10
101
metre 1
Decimetre
0.1
10-1
Centimetre
0.01
10-2
Millimetre
0.001
10-3
Micrometre
10-6
nanometre
10-9

3. Fraction with exponent in denominator
Standard Form
Fraction Form
Fraction with exponent in denominator
Exponential Form 1 _
100
0.1
10-1
0.01
10-2
0.001
10-3
0.0001
10-4

4. To show 10-2, you would have to divide the space between 0 and 10-1 1 -1
10-1
To show 10-2, you would have to divide the space between 0 and 10-1
into 10 places and choose the first spot since 10-2 is 0.01.
This number line is not an appropriate scale
to show these very small numbers.
10-4 would be located in between 0 and 10-2 on this number line.

5. #4 page 248

6. #5 Why is value positive if the exponent is negative?
A negative exponent for a power of 10
shows how many times you should multiply by 0.1.
The number might be very small
but it will never be less than zero.

7. #6 Express 10-8 in standard form.
10-8 =
The negative tells us the number is less than 1.
The digit of the exponent tells us how many zeros!

8. #7 What is the difference between positive and negative exponents?
103 = 10 x 10 x 10 = 1 000
10-3 = 0.1 x 0.1 x 0.1 = 0.001

9. #8 What I understand about negative exponents is:
The number in standard form is in between 0 and 1.
The number used in repeated multiplication is 0.1

10. Check Your Understanding #1 Which value is not equal to the other three?
100 = 1 1
All the rest
are equal to 1!

11. #2 Which value is not equal to the other three?

12. #3 Write in exponential form:

13. #4 Write each power using a positive exponent

14. #5 Write each as a fraction with a power in the denominator
#5 Write each as a fraction with a power in the denominator. Write each fraction as a power with a positive exponent.

15. #6 Find the value of n

16. #7 Copy and complete the statements using x or ÷

17. #8 Order the numbers from least to greatest
#8 Express in exponential form using 10 as the base

18. #9 Find the reciprocal of each, rewrite both in exponential form.

19. #10 Write the power that when multiplied by each number equals 1.
Same question as #9:

20. #11 Write each number in exponential form using a base of 10
a) The People’s Republic of China
has a population greater than people.

21. #11 Write each number in exponential form using a base of 10
b) The mass of an electron
is approximately g.

22. #11 Write each number in exponential form using a base of 10
c) The distance of Venus from the sun
is approximately km.

23. #11 Write each number in exponential form using a base of 10
The diameter of an eyebrow hair is approximately m

24. #12 Explain why 10-4 written in standard form gives a positive number
10-4 means 0.1 x 0.1 x 0.1 x 0.1 which is in standard form
This is not a negative number!

25. #13 An E. coli bacterium has an approximate length of 10-6 m
Write this length using a power with a positive exponent.

26. #13 An E. coli bacterium has an approximate length of 10-6 m
Write this length as a fraction with a power in the denominator.

27. #13 An E. coli bacterium has an approximate length of 10-6 m
How many E. coli bacteria would fit along a 1cm line.
Write this in exponential form.