Attaching Zeros To Finish Dividing
Attaching zeros to finish dividing eliminates remainders in decimal division by extending the dividend with zeros after the decimal point. In Grade 6 Saxon Math Course 1, when a division produces a remainder, place a decimal point in the quotient, attach zeros to the dividend, and continue dividing. For 7 ÷ 4: 4 goes into 7 once (remainder 3), write 1., attach a zero to get 30, 4 goes into 30 seven times (remainder 2), attach another zero to get 20, 4 goes into 20 five times. Answer: 1.75. Decimal answers never use remainders.
Key Concepts
Property Decimal division answers are not written with remainders. Instead, we attach zeros to the end of the dividend and continue dividing.
Examples To solve $0.6 \div 5$, we change it to $0.60 \div 5 = 0.12$. To solve $0.3 \div 4$, we change it to $0.300 \div 4 = 0.075$. To solve $0.7 \div 5$, we change it to $0.70 \div 5 = 0.14$.
Explanation What happens when you can't divide evenly but have no more numbers? Just add a zero to the end of your dividend! Adding a zero does not change the value (0.6 is the same as 0.60), but it gives you more digits to work with so you can finish the division perfectly.
Common Questions
Why do we attach zeros instead of writing a remainder?
Decimal answers require exact values, not remainders. Attaching zeros allows the division to continue until it terminates or a repeating pattern is found.
Calculate 7 ÷ 4 using the attaching-zeros method.
7 ÷ 4 = 1 R3. Write 1. Attach zero: 30 ÷ 4 = 7 R2. Attach zero: 20 ÷ 4 = 5. Answer: 1.75.
Where do you place the decimal point in the quotient?
When you first attach a zero to the dividend (after the decimal point), place a decimal point in the quotient directly above.
Calculate 9 ÷ 8.
9 ÷ 8 = 1 R1. Attach zeros: 10 ÷ 8 = 1 R2, 20 ÷ 8 = 2 R4, 40 ÷ 8 = 5. Answer: 1.125.
What if the division never terminates?
The decimal repeats. For example, 1 ÷ 3 = 0.333... where 3 repeats. Write with a repeating bar: 0.3̄.