Dividing by a Decimal Number
Dividing by a decimal number requires shifting the decimal point in the divisor to make it a whole number, then shifting the decimal point in the dividend the same number of places. For example, 3.35 divided by 0.05 becomes 335 divided by 5 = 67. This technique works because multiplying both the dividend and divisor by the same power of 10 does not change the quotient. Covered in Chapter 5 of Saxon Math Course 2, dividing by decimals is a key 7th grade math skill that students use in unit rate calculations and scientific measurements.
Key Concepts
Property To divide by a decimal number, move the decimal point in the divisor to the right to make it a whole number. Then, move the decimal point in the dividend the same number of places to the right.
Examples $3.35 \div 0.05$ is equivalent to $335 \div 5 = 67$ $0.144 \div 0.8$ is equivalent to $1.44 \div 8 = 0.18$ $21 \div 0.5$ is equivalent to $210 \div 5 = 42$.
Explanation Think of it as a currency swap! Dividing 2.00 dollars by 0.25 dollars is tricky. So, just convert it to 200 cents divided by 25 cents. By shifting the decimal point in both numbers, you get an easier problem with the exact same answer. It's a perfectly legal math cheat code!
Common Questions
How do you divide by a decimal number?
Move the decimal point in the divisor to the right until it becomes a whole number. Then move the decimal point in the dividend the same number of places. Perform the division with the new numbers.
Why do you move the decimal point when dividing by a decimal?
Moving the decimal point is the same as multiplying both numbers by a power of 10. Since multiplying the dividend and divisor by the same number does not change the quotient, the answer stays the same.
What is 21 divided by 0.5?
Move the decimal one place right in both numbers: 210 divided by 5 = 42. So 21 / 0.5 = 42.
What are common mistakes when dividing by decimals?
The most common mistake is moving the decimal in only the divisor but not the dividend, or moving it a different number of places in each. Both numbers must be shifted equally.
How is dividing by a decimal used in real life?
Dividing by a decimal is used to calculate unit prices (e.g., price per ounce), convert measurements, and find rates like speed when time is given as a decimal.
Is dividing by decimals in 7th grade math?
Yes. Saxon Math Course 2 teaches this method in Chapter 5, building on earlier decimal skills and preparing students for more complex calculations with rational numbers.