Dividing Decimals

Dividing decimals builds on long division. The key idea: move the decimal point to turn the divisor into a whole number, then divide normally.

Dividing a Decimal by a Whole Number

When the divisor is already a whole number, place the decimal point in the quotient directly above the decimal point in the dividend, then divide normally.

Example 1: $8.4 \div 4$

$8.4 \div 4 = 2.1$

• $4$ into $8$ = $2$
• Bring the decimal point up
• $4$ into $4$ = $1$

Answer: $2.1$

Example 2: $15.75 \div 5$

• $5$ into $15$ = $3$
• Decimal point comes up
• $5$ into $7$ = $1$ R2
• $5$ into $25$ = $5$

$15.75 \div 5 = 3.15$

Example 3: $0.624 \div 8$

• $8$ into $0$ = $0$
• Decimal point
• $8$ into $6$ = $0$ R6
• $8$ into $62$ = $7$ R6
• $8$ into $64$ = $8$

$0.624 \div 8 = 0.078$

Dividing by a Decimal

When the divisor is a decimal, use this method:

1. Move the decimal point in the divisor to the right until it becomes a whole number
2. Move the decimal point in the dividend the same number of places to the right
3. Divide normally

This works because multiplying both the dividend and divisor by the same power of 10 does not change the quotient.

Example 4: $7.2 \div 0.3$

Step 1: Move the decimal in $0.3$ one place right: $0.3 \rightarrow 3$

Step 2: Move the decimal in $7.2$ one place right: $7.2 \rightarrow 72$

Step 3: Divide: $72 \div 3 = 24$

$7.2 \div 0.3 = 24$

Example 5: $4.56 \div 0.12$

Step 1: Move decimal in $0.12$ two places right: $0.12 \rightarrow 12$

Step 2: Move decimal in $4.56$ two places right: $4.56 \rightarrow 456$

Step 3: $456 \div 12 = 38$

$4.56 \div 0.12 = 38$

Example 6: $3.5 \div 0.25$

Step 1: Move decimal in $0.25$ two places right: $0.25 \rightarrow 25$

Step 2: Move decimal in $3.5$ two places right: $3.5 \rightarrow 350$

Step 3: $350 \div 25 = 14$

$3.5 \div 0.25 = 14$

Example 7: $9.1 \div 0.7$

Move one place right in both: $91 \div 7 = 13$

$9.1 \div 0.7 = 13$

Dividing by Powers of 10

Dividing by 10, 100, or 1,000 moves the decimal point to the left:

$345 \div 10 = 34.5$ $345 \div 100 = 3.45$ $345 \div 1{,}000 = 0.345$

Answers That Don’t Terminate

Sometimes dividing decimals produces a repeating decimal:

Example 8: $1 \div 3$

$1 \div 3 = 0.333... = 0.\overline{3}$

In practice, round to the precision you need: $0.33$ or $0.333$.

Practice Problems

Test your understanding with these problems. Click to reveal each answer.

Key Takeaways

• Dividing by a whole number: place the decimal in the quotient directly above the decimal in the dividend
• Dividing by a decimal: move the decimal right in both divisor and dividend until the divisor is a whole number, then divide
• Dividing by 10, 100, 1000 moves the decimal to the left
• Estimate to check reasonableness — $7.2 \div 0.3$ should be bigger than 7.2 (dividing by a number less than 1 makes the result larger)
• Some divisions produce repeating decimals — round to the needed precision

Return to Arithmetic for more foundational math topics.