Decimal Divide By Decimal Worksheet

Mastering Decimal Division: A Comprehensive Guide with Worksheets

Dividing decimals can seem daunting at first, but with a systematic approach and plenty of practice, it becomes a manageable and even enjoyable skill. This comprehensive guide breaks down decimal division into easy-to-understand steps, providing clear explanations, helpful examples, and downloadable worksheets to solidify your understanding. This article covers everything from the basics of decimal place value to advanced division problems, ensuring you gain a complete mastery of this essential mathematical concept.

Understanding Decimal Place Value

Before diving into division, let's refresh our understanding of decimal place value. Decimals represent parts of a whole number, using a decimal point to separate the whole number from its fractional parts. Each place value to the right of the decimal point represents a decreasing power of ten: tenths (1/10), hundredths (1/100), thousandths (1/1000), and so on.

For example, in the number 3.14159, the 3 represents 3 ones, the 1 represents 1 tenth (0.1), the 4 represents 4 hundredths (0.04), and so forth. Understanding this place value system is crucial for accurately performing decimal division.

Step-by-Step Guide to Dividing Decimals

Dividing decimals involves several key steps. The core concept is to eliminate the decimal point in the divisor (the number you're dividing by) to make the calculation simpler. We achieve this by multiplying both the dividend (the number being divided) and the divisor by a power of 10.

1. Convert the divisor to a whole number:

• Identify the divisor (the number you are dividing by).
• Count the number of decimal places in the divisor.
• Multiply both the divisor and the dividend by 10 raised to the power of the number of decimal places in the divisor. This effectively moves the decimal point in both numbers to the right.

Example:

Let's divide 12.5 by 2.5.

• Divisor: 2.5 (one decimal place)
• Multiply both numbers by 10: 12.5 x 10 = 125 and 2.5 x 10 = 25

2. Perform the division:

Now that the divisor is a whole number, you can perform the division using long division, just as you would with whole numbers.

Example (continuing from above):

Divide 125 by 25:

    5
25 | 125
   -125
     0

Therefore, 125 ÷ 25 = 5

3. Place the decimal point:

The decimal point in the quotient (the answer) should be placed directly above the decimal point in the dividend after the conversion in step 1. Often this is implicitly handled by your process of long division; the placement above is merely a visual affirmation.

Example (continuing from above):

Since we multiplied both numbers by 10, the decimal point in the answer (5) remains to the left of the 5. Therefore, 12.5 ÷ 2.5 = 5.

4. Check your answer:

Multiply the quotient by the divisor. If the result matches the dividend, your calculation is correct.

Example (continuing from above):

5 x 2.5 = 12.5 (This matches the original dividend).

Dealing with Trailing Zeros

Sometimes, the dividend has more decimal places than the divisor. When this happens, you still follow the same steps but remember the final placement of the decimal. This is especially relevant if the dividend ends in trailing zeros.

Example:

Divide 3.200 by 0.8

1. The divisor (0.8) has one decimal place.
2. Multiply both by 10: 32.00 ÷ 8
3. Perform long division: 32.00 ÷ 8 = 4.00
4. The decimal point remains in its original position, relative to the digits after conversion. So the answer is 4.

Note that trailing zeros to the right of the decimal point do not change the value of the number. 4.00 is equal to 4.

Dividing by Powers of 10

Dividing by powers of 10 (10, 100, 1000, etc.) is particularly straightforward. The decimal point simply moves to the left by the number of zeros in the divisor.

• Dividing by 10 moves the decimal one place to the left.
• Dividing by 100 moves the decimal two places to the left.
• Dividing by 1000 moves the decimal three places to the left.

Example:

75.6 ÷ 10 = 7.56 75.6 ÷ 100 = 0.756 75.6 ÷ 1000 = 0.0756

Handling Zeros in the Quotient

Occasionally, you'll encounter situations where you need to add zeros to the dividend to continue the division. This is perfectly acceptable and simply means your quotient will have more decimal places. Remember to add a zero as a placeholder if needed!

Example:

Divide 12 by 25

    0.48
25 | 12.00
   -10.0
     2.00
    -2.00
       0

Here we add zeros to the dividend (12.00) to complete the long division.

Decimal Division Worksheets

Practicing is key to mastering decimal division. Below are sample problems for different skill levels. You can create more problems using similar formats to further enhance your practice.

Worksheet 1: Basic Decimal Division

Divide:

1. 15.6 ÷ 6 =
2. 2.55 ÷ 5 =
3. 3.15 ÷ 0.7 =
4. 0.24 ÷ 0.4 =
5. 7.2 ÷ 0.03 =
6. 1.44 ÷ 1.2 =
7. 5.6 ÷ 0.8 =
8. 0.96 ÷ 0.08 =
9. 21.6 ÷ 1.8 =
10. 6.25 ÷ 2.5 =

Worksheet 2: Intermediate Decimal Division

Divide:

1. 24.75 ÷ 0.25 =
2. 16.8 ÷ 0.12 =
3. 34.56 ÷ 1.2 =
4. 0.875 ÷ 0.05 =
5. 9.75 ÷ 1.5 =
6. 1.368 ÷ 0.32 =
7. 58.08 ÷ 0.36 =
8. 0.792 ÷ 0.048 =
9. 0.63 ÷ 0.007 =
10. 24.64 ÷ 3.2

Worksheet 3: Advanced Decimal Division

Divide:

1. 37.26 ÷ 0.018 =
2. 1.008 ÷ 0.012 =
3. 576.36 ÷ 3.6 =
4. 0.00216 ÷ 0.000072 =
5. 24.76 ÷ 0.058 =
6. 17.01 ÷ 0.046 =
7. 0.00096 ÷ 0.000016 =
8. 315.75 ÷ 0.0025 =
9. 51.84 ÷ 0.009 =
10. 0.0048 ÷ 0.00016 =

Answer Key (Available upon request – creating your own answer key will help reinforce your understanding.)

Frequently Asked Questions (FAQ)

Q: What if I get a repeating decimal in my answer?

A: Repeating decimals are perfectly acceptable. You can either express the answer as a repeating decimal (e.g., 0.333...) or round to a specific number of decimal places, depending on the context of the problem.

Q: Can I use a calculator for decimal division?

A: While calculators are helpful for checking answers, it's crucial to understand the process of decimal division to solve problems effectively and efficiently, especially without technological assistance.

Q: What are some real-world applications of decimal division?

A: Decimal division is used extensively in various fields, including finance (calculating interest, dividing expenses), science (measuring and converting units), engineering (design and calculations), and everyday life (dividing costs among people, calculating fuel efficiency).

Conclusion

Mastering decimal division is a fundamental skill that opens doors to more advanced mathematical concepts. By following the steps outlined in this guide, practicing with the provided worksheets, and asking clarifying questions, you can confidently tackle any decimal division problem. Remember, consistent practice is the key to success. Don't be afraid to make mistakes – they are valuable learning opportunities. With dedication and perseverance, you'll become proficient in this essential mathematical operation.