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Unit 3: Test 1: Multiplying and Dividing Decimals: NBT.2 Study Guide
Multiply and Divide by Powers of Ten.
Getting the Idea.
 To multiply a whole number by a power of 10, add on zeros at the end of the whole
number.
 To multiply a whole number by 10, put one zero at the end of the number.
For example, 12 x 10 = 120
 To multiply a whole number by 100, put two zeros at the end of the number.
For example, 12 x 100 = 1,200
 To multiply a whole number by 1,000, put three zeros at the end of the number.
For example, 12 x 1,000 = 12,000
 Example 1. What is the product?
53 x 10 = ⃝
Strategy: Use mental math. Any whole number multiplied by 10 is the number with one
zero at the end of the number.
Solution: 53 x 10 = 530
 Example 2. Jackie rides her bicycle for 13 miles a day. If she does this for 100 days, how
many miles will she ride in all?
Strategy: Use mental math.
Step 1. Write an equation for the problem. Let m represent the number of miles she will
ride in all.
13 x 100 = m
Step 2. Multiply. Any number multiplied by 100 is the number with two zeros at the end.
13 x 100 = m
13 x 100 = 1,300
Solution: Jackie will ride 1,300 miles in all.
You can write a power of 10 with an exponent. The exponent tells how many times 10 is
used as a factor. For example, 100 is a power of 10 since 10 x 10 = 100. The number 10
is used as a factor 2 times. We write this as 10². You read 10² as ten to the second power
or ten squared.
 Example 3. What is the value of 10⁶?
Strategy: Use a place-value chart that shows powers of 10.
Step 1. Look for a pattern.
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
 Step 2. Identify the pattern. 10¹ evaluates to an answer with 1 zero. 10² evaluates to an
answer with 2 zeros. 10³ evaluates to an answer with 3 zeros. 10⁴ evaluates to an answer
with 4 zeros. 10⁵ evaluates to an answer with 5 zeros.
 Step 3. Apply the patter. 10⁶ will have an answer with 6 zeros. 1,000,000
Solution: The value of 10⁶ is 1,000,000
When multiplying or dividing a decimal by a power of 10, use the exponent to decide how
many places to move the decimal point.
When you multiply by a power of 10, use the exponent to decide how many places to move
the decimal point to the right.
For example,
6.32 x 10¹ = 63.2 - - - - - - - - -move the decimal point one place to the right
6.32 x 10² = 632
- - - - - - - - -move the decimal point two places to the right
6.32 x 10³ = 6,320 - - - - - - - - -move the decimal point three places to the right
When you divide a decimal by a power of 10, use the exponent to decide how many places to
move the decimal point to the left.
For example,
6.32 ÷ 10¹ = 0.632 - - - - - - - - -move the decimal point one place to the left
6.32 ÷ 10² = 0.0632 - - - - - - - - -move the decimal point two places to the left
6.32 ÷ 10³ = 0.00632 - - - - - - - - -move the decimal point three places to the left
 Example 4. What is the product?
0.3 x 10² = ⃝
Strategy: Multiply by a power of 10.
Step 1. Decide in which direction to move the decimal point. You are multiplying by a
power of 10, so you move the decimal point to the right.
Step 2. Find the number of places to move the decimal point in the product. The exponent
tells how many places to move to the right. The exponent is 2, so move the decimal point
2 places.
Step 3. Write the product. Move the decimal point on 0.3 two places to the right. Fill the
empty places with zeros. 0.30.
Solution: 0.3 x 10² = 30
 Example 5. What is the quotient? 627.4 ÷ 10³ = ⃝
Strategy: Divide by a power of 10.
Step 1. Decide in which direction to move the decimal point. You are dividing by a
power of 10, so move the decimal point to the left.
Step 2. Find the number of places to move the decimal point in the quotient. The
exponent tells how many places to move to the left. The exponent is 3, so move the
decimal point 3 places.
Step 3. Write the quotient. Move the decimal point in 627.4 three places to the left. Write
a leading zero. .627.4
Solution: 627.4 ÷ 10³ = 0.6274
Tuesday, November 13, 2012 Parent Signature ______________________________(1-5)
(1) What is 243 multiplied by 10? (A) 24.3 (B) 2,430 (C) 24,300 (D) 243,000
(2) What is 85 multiplied by 0.01? (A) 850 (B) 8.5
(C) 0.85 (D) 0.085
(3) How many zeros are in the product of 11 x 10⁴? __________
(4) How many places to the left do you move the decimal point in 4.8 to find the
quotient of 4.8 ÷ 10²? ____________
(5) Explain what happens to the value of each place as you move from right to left on a
place-value chart. _______________________________________________________
Wednesday, November 14, 2012: Parent Signature____________________________(6-10)
(6) What is the value of 10⁵? _______________
(7) How many zeros are in the product of 84 x 10²? _________________________
(8) What is the quotient? 6.3 ÷ 10³ = ⃝
(9) What is the product? 9.75 x 10⁴ = ⃝
(10)
How many zeros are in the product of 576 x 10⁵? ________
What is the product? _________
Thursday, November 15, 2012: Parent Signature -____________________________(11-15)
(11)
What is the quotient? 8 ÷ 10³ = ⃝
(12)
What is the product? 12 x 10² = ⃝
(13)
DeShawn wrote the number 638,818. How does the value of the 8 in the
thousands place compare to the value of the hundreds place? ___________________
_______________________________________________________________________
(14)
Alice multiplied 87 by a power of ten. She got the product 87,000. By what
power of ten did Alice multiply 87? _________________________________________
_______________________________________________________________________
(15)
Write a number in which the value of 3 in one place is ten times the value of 3
in another place. State the places in your number that have this relationship. _____
_______________________________________________________________________