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Dividing Decimals – Meaning With Examples

Jo-ann Caballes

Updated on January 13, 2024

Welcome to another exciting journey with Brighterly, where we take complex mathematical concepts and transform them into simple, understandable, and enjoyable learning experiences. Today, we will be diving into the fascinating world of dividing decimals. Decimals, those little dots that come after numbers, hold a crucial place in our daily lives. They are there when we measure distances, when we work with money, and when we look at the sizes of our favorite pizza slices. They’re fractional numbers, expressed in the base 10 system, that allow us to represent fractions of a whole number in a way that’s easy to work with.

Dividing decimals might initially seem like a daunting task, filled with numbers, dots, and mathematical rules. But rest assured, with Brighterly by your side, you’ll find that dividing decimals is no more challenging than sharing a cake between friends. It’s all about understanding the process, practicing it, and applying it effectively. So, let’s dive in together and unravel the mystery of dividing decimals!

How to Divide Decimals?

Dividing decimals is similar to dividing whole numbers, with just a few extra steps. The key is to convert the divisor (the number you’re dividing by) into a whole number. You can do this by shifting the decimal point to the right until there are no digits remaining after it. Then, you also shift the decimal point in the dividend (the number you’re dividing) the same number of places. Once the divisor is a whole number, you proceed with the division as normal. After the division, the location of the decimal point in the quotient (the answer) is determined directly above its location in the dividend.

Dividing Decimals by Whole Numbers

Dividing a decimal by a whole number is a straightforward process. It involves the same steps as dividing two whole numbers. You write the decimal (dividend) under the division line (or inside the division box) and the whole number (divisor) outside. Then, you divide as normal, bringing down each digit of the decimal one at a time. The decimal point in the quotient (the answer) is placed directly above its location in the dividend.

Long Division of Decimals

The long division method is another way to divide decimals. This method is particularly useful when the divisor is a large number. It follows the same process as regular long division, but with an extra step of dealing with the decimal point. When doing long division with decimals, you first remove the decimal from the divisor by moving it to the right as many places as necessary until you have a whole number. Then, you move the decimal point in the dividend the same number of places. You place the decimal point in the quotient directly above its new location in the dividend, and proceed with the division as normal.

Division of a Decimal Number by another Decimal

When dividing a decimal by another decimal, you follow a similar process to that of long division of decimals. The goal is to make the divisor a whole number. You do this by moving the decimal point in the divisor to the right as many places as necessary until it becomes a whole number. Then, you do the same with the decimal point in the dividend. After that, you place the decimal point in the quotient directly above its new location in the dividend and proceed with the division as usual.

Dividing Decimals by 10, 100 and 1000

Division by 10

Dividing a decimal by 10 is one of the simplest mathematical operations. It involves shifting the decimal point one place to the left.

Division by 100

Similarly, dividing a decimal by 100 involves moving the decimal point two places to the left.

Division by 1000

And, you guessed it, dividing a decimal by 1000 involves shifting the decimal point three places to the left.

Dividing Decimals Examples

Let’s go through some examples to demonstrate these concepts:

1. Dividing the decimal 0.75 by the whole number 3:

   0.75 ÷ 3 = 0.25

2. Using long division to divide 1.36 by 0.4:

   1.36 ÷ 0.4 = 3.4

3. Dividing a decimal by another decimal, for example, 0.48 ÷ 0.2:
   0.48 ÷ 0.2 = 2.4
4. Dividing a decimal by 10:
   0.57 ÷ 10 = 0.057

5. Dividing a decimal by 100:
   0.57 ÷ 100 = 0.0057

Practice Questions on Dividing Decimals

To further understand the concept of dividing decimals, it’s a good idea to practice with some problems. Try these:

1. 0.64 ÷ 8
2. 1.75 ÷ 0.5
3. 0.006 ÷ 1000
4. 1.36 ÷ 0.4
5. 0.0025 ÷ 10

Conclusion

As we wrap up our adventure into the world of dividing decimals, we at Brighterly hope that this journey has transformed what might initially have seemed like a complex concept into a clear and manageable one. It’s essential to remember that math is not about memorization but about understanding the process. Dividing decimals might seem intricate at first, but like many things in life, with consistent practice and the correct approach, it becomes an intuitive process.

Recall that the heart of the process lies in transforming the divisor into a whole number by appropriately shifting the decimal point, and applying the same shift to the dividend. This simple yet effective trick turns the problem into a familiar whole number division problem. With the divisor as a whole number, you proceed with the division, just as you would do with whole numbers.

And remember, every new concept you master is a step forward in your mathematical journey. At Brighterly, we’re here to guide and support you every step of the way. So keep practicing, keep exploring, and keep growing brighter with Brighterly!

Frequently Asked Questions on Dividing Decimals

What is the trick to dividing decimals?

The trick to dividing decimals lies in simplifying the problem by turning it into a whole number division problem. This is done by shifting the decimal point of the divisor (the number you’re dividing by) to the right until it becomes a whole number. This movement of the decimal point is also applied to the dividend (the number to be divided). The shifted decimal point in the dividend effectively multiplies it by a power of 10 without changing its actual value. After this transformation, you can proceed with the division just as you would with whole numbers. The final step is to place the decimal point in the quotient (the result) directly above its location in the dividend, thus ensuring the correct answer.

How do you divide decimals step by step?

Here’s a step-by-step guide to dividing decimals:

1. Write down the problem with the dividend (the number to be divided) under the division bar and the divisor (the number you’re dividing by) outside.

2. Shift the decimal point in the divisor to the right until the divisor becomes a whole number. Count how many places you moved it.

3. Shift the decimal point in the dividend the same number of places to the right. This might involve adding zeros to the end of the dividend.

4. Now that the divisor is a whole number, you can proceed with the division as if you were dividing by a whole number. Start from the left of the dividend and divide each digit or group of digits by the divisor, writing the result above the division bar.

5. Place the decimal point in the quotient (the result) directly above its location in the dividend.

6. Continue the division process until you’ve divided all the digits of the dividend.

How do you divide decimals by 10, 100, and 1000?

Dividing decimals by 10, 100, and 1000 is an easy task once you understand the concept of place value in the decimal system. Here’s how it works:

1. When dividing a decimal by 10, shift the decimal point one place to the left. This is equivalent to reducing the value of each digit by one place value. For instance, if you’re dividing 0.75 by 10, you shift the decimal point one place to the left to get 0.075.

2. When dividing a decimal by 100, shift the decimal point two places to the left. In this case, each digit reduces its place value by two places. For instance, if you’re dividing 0.75 by 100, you shift the decimal point two places to the left to get 0.0075.

3. When dividing a decimal by 1000, shift the decimal point three places to the left. Here, each digit reduces its place value by three places. For example, if you’re dividing 0.75 by 1000, you shift the decimal point three places to the left to get 0.00075.

Jo-ann Caballes

5 articles

As a seasoned educator with a Bachelor’s in Secondary Education and over three years of experience, I specialize in making mathematics accessible to students of all backgrounds through Brighterly. My expertise extends beyond teaching; I blog about innovative educational strategies and have a keen interest in child psychology and curriculum development. My approach is shaped by a belief in practical, real-life application of math, making learning both impactful and enjoyable.