Dividing by a Decimal Number
Dividing by a decimal number is simplified by converting the divisor to a whole number: multiply both the dividend and divisor by the same power of 10 (10, 100, or 1000) to shift the decimal point rightward. In Grade 6 Saxon Math Course 1 (Chapter 5: Number and Operations), students count the decimal places in the divisor, multiply both numbers by 10 raised to that count, then divide normally. For 7.2 ÷ 0.4: multiply both by 10 to get 72 ÷ 4 = 18. For 3.6 ÷ 0.12: multiply both by 100 to get 360 ÷ 12 = 30. The quotient is unchanged because multiplying dividend and divisor by the same value is equivalent to multiplying the fraction by 1.
Key Concepts
New Concept When the divisor of a division problem is a decimal number, we change the problem so that the divisor is a whole number. This is done by forming an equivalent division problem. What’s next This card introduces the core strategy. Next, you'll master this method through worked examples and tackle challenge problems involving decimal division.
Common Questions
How do you divide by a decimal number?
Count the decimal places in the divisor. Multiply both dividend and divisor by 10 raised to that count to make the divisor a whole number. Then divide normally.
Calculate 7.2 ÷ 0.4.
0.4 has 1 decimal place. Multiply both by 10: 72 ÷ 4 = 18.
Calculate 3.6 ÷ 0.12.
0.12 has 2 decimal places. Multiply both by 100: 360 ÷ 12 = 30.
Why does multiplying both numbers by the same power of 10 not change the answer?
Because it is equivalent to multiplying the fraction (dividend/divisor) by 10/10 = 1, which does not change its value.
How do you divide 5 by 0.25?
0.25 has 2 decimal places. Multiply both by 100: 500 ÷ 25 = 20.