Dividing by Powers of 10
Dividing by powers of 10 works by shifting the decimal point to the left by the number of places equal to the exponent. Dividing 3.5 by 10 to the 4th power moves the decimal 4 places left, giving 0.00035. This Grade 7 math skill from Saxon Math, Course 2 is the inverse of multiplying by powers of 10 and is foundational for scientific notation, unit conversions in the metric system, and any calculation involving very small decimal values in science and engineering.
Key Concepts
Property To divide a number by a positive power of 10, we shift the decimal point to the left the number of places that is indicated by the exponent. By doing this you will see that the number gets much smaller, which is the opposite of multiplying powers of 10.
Examples $3.5 \div 10^4 = 0.00035$ $12.5 \div 10^3 = 0.0125$ $4.8 \div 10^4 = 0.00048$.
Explanation Dividing by a power of 10 is like using a shrink ray on your number! The exponent reveals how many spots to shift the decimal point to the left, making the number tinier. This is a very useful shortcut to have when you want to make a number much smaller.
Common Questions
How do I divide a number by a power of 10?
Move the decimal point to the left by as many places as the exponent. For example, 12.5 divided by 10 to the 3rd is 0.0125 — move the decimal 3 places left.
Why does dividing by a power of 10 move the decimal left?
Multiplying by 10 moves the decimal right (number gets bigger), so dividing by 10 does the opposite — moves it left (number gets smaller), because division is the inverse of multiplication.
How is dividing by powers of 10 used in real life?
Scientists use this when converting large metric measurements to smaller units, or when working with very small numbers in chemistry and physics expressed in scientific notation.
What is the difference between multiplying and dividing by powers of 10?
Multiplying by 10^n moves the decimal n places to the right, making the number larger. Dividing by 10^n moves it n places to the left, making the number smaller.
When do students learn to divide by powers of 10?
This skill is typically introduced in Grade 6 and reinforced in Grade 7. Saxon Math, Course 2 covers it in Chapter 4 alongside multiplication by powers of 10.
What are common mistakes when dividing by powers of 10?
Students sometimes move the decimal in the wrong direction (right instead of left) when dividing, confusing it with multiplication by powers of 10. Remember: dividing makes numbers smaller.
How does dividing by powers of 10 connect to scientific notation?
Numbers in scientific notation with negative exponents (like 5.12 times 10 to the -7) result from dividing by large powers of 10. Understanding decimal shifting makes scientific notation intuitive.