Dividing decimals by whole numbers and powers of 10

Idea

Decimal $\div$ whole number. Perform long division as usual. Place the decimal point in the quotient directly above the decimal point in the dividend.

Example: $7.2 \div 3$. Long division: $72 \div 3 = 24$. Reinsert the point: $7.2 \div 3 = 2.4$. (The dividend has $1$ decimal place; so does the quotient.)

If the dividend doesn't divide exactly, add zeros after the decimal point and continue. Example: $1 \div 4$ , write $1$ as $1.00$, then divide: $1.00 \div 4 = 0.25$.

Decimal $\div$ power of $10$. Shift the decimal point to the left by as many places as the power of $10$:

• $\div 10$: shift left by $1$. $34.56 \div 10 = 3.456$.
• $\div 100$: shift left by $2$. $34.56 \div 100 = 0.3456$.
• $\div 1000$: shift left by $3$. $34.56 \div 1000 = 0.03456$.

If you run out of digits, add zeros to the left of the decimal point as needed.

The reason: dividing by $10$ moves every digit one column to the right , equivalently, the decimal point one column to the left.

Worked examples

Example 1. Compute $5.6 \div 7$.

$56 \div 7 = 8$. Insert point: $5.6 \div 7 = 0.8$.

Example 2. Compute $12.5 \div 5$.

$125 \div 5 = 25$. Insert point: $12.5 \div 5 = 2.5$.

Example 3. Compute $34.5 \div 100$.

Shift point left by $2$: $0.345$.

Example 4. Compute $0.7 \div 10$.

Shift point left by $1$: $0.07$.

Try it yourself

1. Compute $4.8 \div 6$.
2. Compute $9.3 \div 3$.
3. Compute $1.25 \div 5$.
4. Compute $7.5 \div 10$.
5. Compute $245.6 \div 100$.
6. Compute $0.5 \div 100$.
7. Compute $9 \div 4$ (as a decimal).
8. Compute $36.4 \div 7$.

Activity

On graph paper, write a $4$-digit decimal. Use a pencil to literally move the decimal point left or right as you divide or multiply by powers of ten. Internalise the "shift" idea.