Multiplying And Dividing Decimals
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3Unit 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.
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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
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