Multiplying by Powers of 10
Multiplying by powers of 10 is a decimal shortcut: multiplying by 10 moves the decimal point one place right, multiplying by 100 moves it two places right, and multiplying by 1000 moves it three places right. For 3.47 x 100 = 347. Dividing by a power of 10 reverses the direction. This 6th grade math skill from enVision Mathematics Grade 6 is the foundation for scientific notation, metric unit conversion, and any calculation that scales a number up or down by a factor of ten.
Key Concepts
Property To multiply a number by a positive integer power of 10, $10^n$, move the decimal point $n$ places to the right. Add zeros as placeholders if needed.
Examples $2.6 \times 10^5 = 2.6 \times 100,000 = 260,000$ $7 \times 10^3 = 7 \times 1,000 = 7,000$ $0.45 \times 10^2 = 0.45 \times 100 = 45$.
Explanation Multiplying by powers of 10 is a way to write very large numbers concisely. The exponent on the 10 tells you how many places to move the decimal point to the right. This is because each power of 10 adds another zero, making the number ten times larger. This skill is a foundational concept for understanding scientific notation.
Common Questions
How do you multiply a number by a power of 10?
Move the decimal point to the right by the number of zeros in the power of 10. For 3.47 x 100: move the decimal 2 places right to get 347.
How do you multiply by 10, 100, and 1000?
By 10: move decimal 1 place right. By 100: move decimal 2 places right. By 1000: move decimal 3 places right. For 2.5 x 1000 = 2500.
What happens when you divide by a power of 10?
Move the decimal point to the left. Dividing by 100 moves it 2 places left. For 347 / 100 = 3.47.
What grade learns multiplying by powers of 10?
Multiplying by powers of 10 is a 6th grade skill in enVision Mathematics Grade 6, foundational to decimal operations and scientific notation.
How does multiplying by powers of 10 connect to scientific notation?
Scientific notation writes large numbers as a decimal times a power of 10 (e.g., 3.47 x 10 squared = 347). Multiplying by the power of 10 converts it back to standard form.
Does this rule work for negative powers of 10?
Yes. Multiplying by 10 to the negative 2 (= 0.01) moves the decimal 2 places left, which is the same as dividing by 100.