1. Multiplying by Powers of base ten
NBT.2

2. Learning Target
I can determine the product when a decimal is multiplied by a power of 10. I can recognize that my digits shift when I multiply by a power of 10.
Repeat after me.

3. Our goal Complete the equations. 9.08x 10= 13x100= 0.5x100=

4. Powers of Ten
Numbers like 10, 100, or 1,000 that can be written as products of tens are called powers of ten.
Multiplying or dividing by powers of ten is related to place value.
When we multiply, we increase the value of the number. What direction do we associate with increasing?

5. What do you notice is happening?
Think about this…..
Patterns can help you understand multiplying powers of ten.
Thousands
Hundreds
Ten
Ones 3
The teacher will model how you multiply by ten to reach the next number.

6. Think about this….
What is happening when we multiply decimals by a power of ten?
Ones
Tenths
Hundredths
Thousandths .0 3 .3
The teacher will model how you multiply by ten to reach the next number.

7. Analyze these patterns
8x1=8
8x10=80
8x100=800
8x1,000=8,000
0.009x1=0.009
0.009x10=0.09
0.009x100=0.9
0.009x1,000=9
What do you notice is happening with the zeros?
What appears to be happening with the 9?

8. Multiplying by powers of Ten
grade-math/cc-5th-place-value-decimals-top/cc- 5th-mult-div-decimals /a/multiplying-by

9. How can I be certain that I am following the pattern correctly?
You Watch Me
How can I be certain that I am following the pattern correctly?
Shifting the Digits
0.9x1=
0.9x10=
0.9x100=
0.9x1,000=
Thousands
Hundreds
Tens
Ones .
Tenths
Hundredths
Thousandths

10. How can I be certain that I am following the pattern correctly?
You Watch Me
How can I be certain that I am following the pattern correctly?
Moving the decimal
0.9x1=
0.9x10=
0.9x100=
0.9x1,000=

11. Work with Me Complete the patterns. 15x10= 15x100= 15x1,000= 1.5x1=
What do the digits do each time I multiply?
Complete the patterns.
15x10=
15x100=
15x1,000=
1.5x1=
1.5x10=
1.5x100=
1.5x1,000=
What is written in word form?

12. What happens to the digits as we multiply by Powers of Ten?
You Try & I will help
What happens to the digits as we multiply by Powers of Ten?
1.) Complete the patterns.
37x10=
37x100=
37x1,000=
2.) Complete the patterns.
0.005x1=
0.005x10=
0.005x100=
0.005x1,000=
True OR False
9 is 10 times as much as 0.9

13. Try a Few then check with your partner
Complete the equation.
1.) 432 x 100=
2.) x 1,000=
3.) 7.87 x 10=
4.) 21.9 x 1,000=
43,200
285
0.787
0.0219
What could you change to make this true?
90 is 10 times as much as 0.9

14. Try a Few More then check with your partner
Complete the equation.
60.8 x 10=
27 x 100=
0.33 x 1,000=
509.4 x 1,000=
608
0.27
330
0.5094
What is (2 x 10) + (3 x 1/10) + (4 x 1/100) written in word form?

15. Talk about It!!
When I multiply by 10, my digits shift to the left _____ times because the value is _________.
When I multiply by 100, my digits shift to the left _____ times because the value is ________.
When I multiply by 1,000, my digits shift to the left ______ times because the value is _______.  
How many shifts/hops do you make when you multiply by 10,000? How do you know?

16. Evaluate my work
I believe that every time you multiply a number by ten you just add a zero to the end of the number.
For example, 6x10=60.
Is my claim ALWAYS true?
Would it ever be false?
If you agree with my claim, say, “ready to rock”. If not, drop the mic.

17. PROVE IT!!! Learning Target
Can you determine the product of a decimal when you multiply it by a power of ten?
Can you recognize the movement of the digit AND decimal when you multiply by a power of ten?
PROVE IT!!!

18. Exit ticket Complete the equations. 1.) 9.08 x 10= 2.) 13 x 100=
Fill in the blanks.
5.) When I multiply by Powers of Ten, my digits shift to the __________ because I am ___________ the value.
6.) When I multiply by 1,000, each digit shifts ______ places.
7.) When I multiply by 100, each digit shifts _______ places.
8.) When I multiply by 10, each digit shifts _______ places.