Multiply Greater Number by Powers of 10
Key Concepts
- Use pattern and mental math to multiply a whole number by a power of 10
Multiply greater number by powers of 10
A power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times.
The first few non-negative powers of ten are: 1, 10, 100, 1,000, 10,000, 100,000, 1,000,000,
10,000,000.
Below image express expanded form and exponents of 10.
Below image indicates the power of 10.
For example:
The place value chart shows relationship for the number 4.
Use pattern and mental math to multiply a whole number by a power of 10
Example 1:
Power of 10 using place value relationship:
Find 26 x 10, 000 by using place value relationships.
Solution:
Multiply 26 by 1; 10; 100 and 10, 000;
26 x 1 = 26 ones = 26
26 x 10 = 26 tens = 260
26 x 100 = 26 hundreds = 2,600
26 x 1,000 = 26 thousands=26, 000
26 x 10, 000 = 26 ten thousand =260,000
Pattern
Power of 10 using exponents
Exponent:
An exponent tells how many times a number is multiplied
by itself.
10×10×10×10×10×10×10×10×10
1,000,000,000
Find 26 x 10, 000 by using exponents.
Solution:
Multiply 26 by 1; 10; 100 and 10, 000;
26 x 1 = 26 x 100 =26
26 x 10 = 26 x 10 1 = 260
26 x 100 = 26 x 102 = 2,600
26 x 1,000 = 26 x 103=26, 000
26 x 10, 000 = 26 x 104 = 260,000
Example 2:
Power of 10 using place value relationship:
Find 67 x 10, 000 by using place value relationships.
Solution:
Multiply 67 by 1; 10; 100 and 10, 000;
67 x 1 = 67 ones =67
67 x 10 = 67 tens = 670
67 x 100 = 67 hundreds = 6,700
67 x 1,000 = 67 thousands=67, 000
67 x 10, 000 = 67 ten thousand =670,000
Pattern
Power of 10 using exponents.
Find 67 x 10, 000 by using exponents.
Solution:
Multiply 67 by 1; 10; 100 and 10, 000;
67 x 1 = 67 x 100 = 67
67 x 10 = 67 x 10 1 = 670
67 x 100 = 67 x 102 = 6,700
67 x 1,000 = 67 x 103 = 67, 000
67 x 10, 000 = 67 x 104 = 670,000
Example 3:
Find 8 x 1,000 using exponent form.
Exercise
- Find each product.
- 34 × 1
- 34 × 10
- 34 × 100
- 1, 000
- Find the value of the following exponents.
- 42 × 1
- 42 × 101
- 42 × 102
- 42 × 103
- Use reasoning to fill in the missing numbers.
- 245 × 104= ____________.
- 16 × ________ = 16,000.
- Explain how to find the product of 80 × 104.
- Find the product of 60 × 10,000.
- How many zeros will there be in the product of 17 × 1, 000?
- Rewrite the following numbers using powers of ten.
For example, 800 = 8 × 102
- 9,000
- 70,000
- 8,000,000
- If a Robert house manufactures 100 T-Shirts in a day. How many shirts were manufactures in the month of November?
- Match the powers of 10.
- If a Kara runs 10 miles in a day. How many miles Kara runs in 60 days?
- How many zeros will there be in the product of 19 x 10, 000?
Concept Map
What have we learned
- Understand Multiply greater number by powers of 10.
- Understand how to use pattern and mental math to multiply a whole number by a power of 10.
- Understand how to multiply Power of 10 using place value relationship.
- Understand exponent.
- Understand how to multiply Power of 10 using exponents.
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