1. called supernaturallyby
Multiply
Divide
Powers
and
I have a
special power. It’s
called supernaturally
good looks. of T en
Multiply and divide decimals and fractions, using efficient and generalizing procedures, including standard algorithms.

2. I can…
Multiply and Divide by Whole Number powers of 10
Multiply and Divide by Decimal powers of 10
Self Assessment
5- I can do it without help & teach others.
4- I can do this with no help, but I don’t know if I can explain it.
3- I can do this with a little help.
2- I can do this with a lot of help!
1- I don’t have a clue.

3. Ricki’s Rocko Taco…now that’s where I place some value!
Powers of 10
Before we learn to multiply and divide by Powers of 10, we need to review place value.
Ricki’s Rocko Taco…now that’s where I place some value! 1 2
Okay!
I’ll try! 3
Place Value – The value of a digit depending on its place or position in a number.
“Let’s just focus on numbers for awhile, Sparky!”

4. Can you name all of the place values in the number below?
Powers of 10
Can you name all of the place values in the number below?
hundred thousands
ten thousandths
ten thousands
thousandths
thousands
hundredths
millions
hundreds
tenths
ones
tens
and
8, 374,
0.1
0.01
0.001
0.0001

5. Powers of 10
Notice! As we move to the left on the place value chart, we multiply by 10 to get to each next place.
It makes sense! When you multiply, numbers get bigger. When you divide, numbers get smaller.
And as we move to the right, we divide by 10 to get to each next place.
÷ 10
÷ 10
÷ 10
÷ 10
ten thousandths
ten thousands
thousandths
÷ 10
thousands
hundredths
÷ 10
hundreds
÷ 10
÷ 10 .
tenths
ones
tens
× 10
× 10
× 10
× 10
× 10
× 10
× 10
× 10
𝟏 𝟏𝟎
𝟏 𝟏𝟎𝟎
𝟏 𝟏,𝟎𝟎𝟎
𝟏 𝟏𝟎,𝟎𝟎𝟎
10,000
1,000
100 10 1

6. Pronounced “ten to the third power”
Powers of 10
Example:
In math, a Whole Number Power of 10 is any integer power of the number ten.
power or exponent
10 3
base number
Or ten multiplied by itself 3 times.
Pronounced “ten to the third power”
𝟏𝟎 𝟑 =𝟏𝟎 × 10 × 𝟏𝟎 = 1,000

7. Powers of 10 Do you see a pattern?
Here are a few whole number powers of 10:
Do you see
a pattern?
𝟏𝟎 𝟏 =𝟏𝟎
𝟏𝟎 𝟐 =𝟏𝟎×𝟏𝟎=𝟏𝟎𝟎
𝟏𝟎 𝟑 =𝟏𝟎×𝟏𝟎×𝟏𝟎=𝟏,𝟎𝟎𝟎
𝟏𝟎 𝟒 =𝟏𝟎×𝟏𝟎×𝟏𝟎×𝟏𝟎=𝟏𝟎,𝟎𝟎𝟎
𝟏𝟎 𝟓 =𝟏𝟎×𝟏𝟎×𝟏𝟎×𝟏𝟎×𝟏𝟎=𝟏𝟎𝟎,𝟎𝟎𝟎
𝟏𝟎 𝟔 =𝟏𝟎×𝟏𝟎×𝟏𝟎×𝟏𝟎×𝟏𝟎×𝟏𝟎=𝟏,𝟎𝟎𝟎,𝟎𝟎𝟎
If you said that each exponent equals the number of zeros in each product, you’re right!

8. Powers of 10 In other words:
When you multiply by a whole number power of 10, move the decimal point to the right the same number of places as there are zeros in the power of 10.
In other
words:
-Multiplying by 10 moves the
decimal 1 place to the right.
-Multiplying by 100 moves the
decimal 2 places to the right.
And so on…

9. really likes that shorty cut!
Powers of 10
This pattern creates a shortcut when we multiply any whole number by a power of ten!
Instead of actually multiplying, we can simply count the number of zeros in 100,000 (which equals 𝟏𝟎 𝟓 ), and add that many zeros to 279.
Check out the following multiplication problem!
279 × 100,000
= 27,9
00,000
Sparky
really likes that shorty cut!
Next slide please!
Speaking of short things…

10. Powers of 10 Let’s try some! 1) 415 × 1,000 = 415,000 2) 1,000,000
Multiply the following, using the Powers of 10 rule.
Let’s try some!
1) 415 × 1,000 =
415,000
2) 1,000,000 ×
56,000,000 3)
× 100
4) 421 × 10 =
4,210
23,300 6)
× 100,000
5) 10,000 × 77 =
770,000
88,900,000

11. Powers of 10 . . . . Let’s try some more! 1) 0.05 × 1,000 = 0. 0 5
1) × 1,000 =
0. 0 5
= 50 1 2 3 .
2) × 100 =
= 607 1 2 . .
3) 1,000 × 509 =
509
590,000 1 2 3

12. Powers of 10 Your Turn…. 2) 100,000 × 1.25529 1) 0.813 × 100 = 81.3
Multiply the following decimals by simply moving each decimal the correct number of places.
Your Turn….
2) ,000 ×
1) × 100 =
81.3
125,529 3)
× 10,000
4) × 1,000 =
850
900,000
6) ,000,000 ×
5) 10 × =
5,468.21
79,000,000

13. Powers of 10 In other words:
When you multiply by a decimal power of 10, move the decimal point to the left the same number of places as there are zeros in the power of 10.
In other
words:
-Multiplying by 0.1 moves the
decimal 1 place to the left.
-Multiplying by 0.01 moves the
decimal 2 places to the left.
And so on…

14. Powers of 10 . . . Let’s try some! 1) 95.38 × 0.001 = 9 5.38 = 0.09538
1) × =
9 5.38 = 3 2 1 . =
2) × 0.01 = 2 1 .
3) × 4.53 =
4 . 53 3 2 1

15. Powers of 10 Your Turn…. 2) 63.65 × 0.1 1) 459.1 × 0.01 = 4.591 6.365
Multiply the following decimals by simply moving each decimal the correct number of places.
Your Turn…. 2) ×
1) × 0.01 =
4.591
6.365 3) ×
4) × 0.1 =
0.085
0.1246

16. Powers of 10 In other words:
When you divide by a whole number power of 10, move the decimal point to the left the same number of places as there are zeros in the power of 10.
In other
words:
-Dividing by 10 moves the
decimal 1 place to the left.
-Dividing by 100 moves the
decimal 2 places to the left.
And so on…

17. Powers of 10 . . . Let’s try some! 1) 85.38 ÷ 1000 = = 0.08538 8 5.38
1) ÷ 1000 = =
8 5.38 3 2 1 . =
2) ÷ 100 = 2 1 .
3) 35 ÷ 100 =
3 5
0.35 2 1

18. Powers of 10 Your Turn…! 1) 38.95 ÷ 100 = 2) 401.14 ÷ 10,000 = 0.3895
Divide the following decimals by simply moving each decimal the correct number of places.
Your Turn…!
1) ÷ 100 =
2) ÷ 10,000 =
0.3895
3) ÷ 10 =
4) 5.1 ÷ 1,000,000 =
9.37
5) 682 ÷ 1,000 =
6) 2,393.7 ÷ 100,000 =
0.682

19. Powers of 10 In other words:
When you divide by a decimal power of 10, move the decimal point to the right the same number of places as there are zeros in the power of 10.
In other
words:
-Dividing by 0.1 moves the
decimal 1 place to the right.
-Dividing by 0.01 moves the
decimal 2 places to the right.
And so on…

20. Powers of 10 . . . . Let’s try some! 1) 0.05 ÷ 0.001 = 0. 0 5 = 50
1) ÷ =
0. 0 5
= 50 1 2 3 .
2) ÷ 0.01 =
= 607 1 2 . .
3) 509 ÷ =
509
590,000 1 2 3

21. Powers of 10 Your Turn…. 1) 459.1 ÷ 0.01 = 45,910 2) 0.85 ÷ 0.1 = 8.5
Multiply the following decimals by simply moving each decimal the correct number of places.
Your Turn….
1) ÷ 0.01 =
45,910
2) ÷ 0.1 =
8.5
3) 5 ÷ 0.1 = 50
4) 3.2 ÷ =
3200

22. If you can count, YOU CAN DO THIS!
Powers of 10
Whole number power of 10
Multiply -- just move the decimal point to the right. . →
Divide -- move the decimal point to the left. . ←
If you can count, YOU CAN DO THIS!

23. If you can count, YOU CAN DO THIS!
Powers of 10
Decimal number power of 10
Divide -- just move the decimal point to the right. . →
Multiply -- move the decimal point to the left. . ←
If you can count, YOU CAN DO THIS!

24. I can…
Multiply and Divide by Whole Number powers of 10
Multiply and Divide by Decimal powers of 10
Self Assessment
5- I can do it without help & teach others.
4- I can do this with no help, but I don’t know if I can explain it.
3- I can do this with a little help.
2- I can do this with a lot of help!
1- I don’t have a clue.

25. Show your work by moving your decimals points!
Daily Check 4.5
in your math notebook
Show your work by moving your decimals points!
27 x
27 ÷
0.105 x 10,000
0.105 ÷ 10,000
A recycling plant celebrated when it processed the one millionth bag of used newsprint. If the average weight of a bag of newsprint is pounds, how many pounds of newsprint had been recycled?