Dividing Decimal Numbers
Dividing decimal numbers in Grade 7 uses long division, keeping the decimal point in the quotient directly above the decimal point in the dividend. In Saxon Math, Course 2, students divide numbers like 9.2 ÷ 4 = 2.3 by treating the decimal point as a position marker that carries through to the answer. When dividing by a decimal divisor, multiply both dividend and divisor by the same power of 10 to make the divisor a whole number first. This skill is used constantly in science, measurement, cooking, and financial calculations.
Key Concepts
Property When we use long division, the decimal point in the quotient is lined up with the decimal point in the dividend.
Examples $9.2 \div 4 \rightarrow \begin{array}{r} 2.3 \\ 4 \overline{) 9.2} \\ 8\phantom{.} \\ \hline 1\phantom{.}2 \\ 1\phantom{.}2 \\ \hline 0 \end{array}$ $1.4 \div 5 \rightarrow \begin{array}{r} 0.28 \\ 5 \overline{) 1.40} \\ 1\phantom{.}0\phantom{0} \\ \hline 40 \\ 40 \\ \hline 0 \end{array}$ $0.0245 \div 5 \rightarrow \begin{array}{r} 0.0049 \\ 5 \overline{) 0.0245} \\ 20\phantom{5} \\ \hline 45 \\ 45 \\ \hline 0 \end{array}$.
Explanation It’s the 'bring it straight up' rule! In long division, just move the decimal point from the number inside the box straight up into your answer line. Then, divide like normal. If you run out of digits, add a zero to the end and keep dividing until you are finished.
Common Questions
How do you place the decimal point when dividing decimals?
Align the decimal point in the quotient directly above the decimal point in the dividend. The position is set before you begin dividing the digits.
How do you divide a decimal by a whole number?
Perform long division as normal, but place the decimal point in the quotient directly above its position in the dividend. For example, 9.2 ÷ 4 = 2.3.
How do you divide by a decimal divisor?
Multiply both the dividend and divisor by the power of 10 that makes the divisor a whole number. For example, 1.4 ÷ 0.2 → multiply both by 10 → 14 ÷ 2 = 7.
What if there is a remainder when dividing decimals?
Add a zero to the right of the last decimal digit in the dividend and continue dividing. You can add as many zeros as needed to reach the desired precision.
Where is dividing decimal numbers taught in Saxon Math Course 2?
This skill is introduced in Saxon Math, Course 2, as part of Grade 7 decimal operations and number sense content.
Why is decimal placement so important in decimal division?
A misplaced decimal changes the answer by a factor of 10, 100, or more. Aligning it correctly is critical for getting an accurate quotient.
What common mistakes do students make when dividing decimals?
Students often forget to place the decimal in the quotient, or place it incorrectly by counting digits rather than aligning with the dividend's decimal position.