Multiplying by Powers of 10
Multiplying a number by a positive power of 10 shifts the decimal point to the right by as many places as the exponent. Multiplying 3.7 by 10 to the 3rd moves the decimal 3 places right, giving 3,700. This Grade 7 math skill from Saxon Math, Course 2 is the inverse of dividing by powers of 10 and is essential for metric unit conversions, scientific notation, and understanding place value relationships — whenever a number is expressed as a product involving 10, you are using this rule.
Key Concepts
Property To multiply a decimal number by a positive power of 10, we shift the decimal point to the right the number of places that is indicated by the exponent. This simple trick is an easy way to make the number get much bigger, much faster! It’s a very useful tool.
Examples $46.235 \times 10^2 = 4623.5$ $25 \times 10^6 = 25,000,000$ $2.5 \text{ million} = 2.5 \times 10^6 = 2,500,000$.
Explanation Multiplying by a power of 10 is like giving your number a giant growth spurt! The exponent tells you exactly how many places you need to slide the decimal point over to the right. By doing this you are making your number instantly bigger, which is a neat trick to have.
Common Questions
How do I multiply a number by a power of 10?
Move the decimal point to the right by the number of places equal to the exponent. For example, 4.56 times 10 squared = 456 (move decimal 2 places right).
What happens when you multiply by 10 to the 4th?
Move the decimal 4 places to the right, adding zeros as needed. For example, 1.2 times 10 to the 4th = 12,000.
Why does multiplying by a power of 10 move the decimal to the right?
Each factor of 10 makes the number 10 times larger, which moves the decimal one place right in our base-10 number system.
How is multiplying by powers of 10 the opposite of dividing?
Multiplying by 10 to the n moves the decimal n places right (larger number). Dividing by 10 to the n moves the decimal n places left (smaller number). They are inverse operations.
When do students learn to multiply by powers of 10?
This skill is introduced in Grade 5-6 and reinforced in Grade 7. Saxon Math, Course 2 covers it in Chapter 4 alongside scientific notation and metric conversions.
What are common mistakes when multiplying by powers of 10?
Students sometimes move the decimal in the wrong direction (left instead of right) when multiplying, confusing it with division. Remember: multiplication makes numbers bigger, so the decimal goes right.
How does multiplying by powers of 10 connect to scientific notation?
Converting scientific notation to standard form uses this skill. For 3.5 times 10 to the 6, move the decimal 6 places right to get 3,500,000.