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# How to Multiply Decimals?

Multiplying decimals is a mathematical operation that involves multiplying numbers with decimal points.

Imagine a scenario where you’re dealing with measurements that aren’t just whole units but also include fractional parts, or picture a situation where you need to calculate the total cost of items with prices that extend beyond whole dollars.

In real-life situations, multiplying decimals helps you find precise solutions to a wide range of problems.

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Multiplying Decimals with Whole Numbers

Multiplying decimals with whole numbers is like multiplying whole numbers but involves an additional consideration for decimal places. Here are the key differences and steps when multiplying decimals with whole numbers compared to multiplying whole numbers:

Step 1: Multiply as if Whole Numbers

Treat the decimal number as if it were a whole number and multiply it by the whole number just as you would with two whole numbers.

Example

3.2

x   5

—–

160   (32 multiplied by 5)

Step 2: Adjust the Decimal Point

Count the decimal places in the decimal number (3.2, in this case, has one decimal place). This number will indicate how many decimal places the final product should have.

Place the decimal point in the product by counting from the right of the result, starting with the last digit. Count as many decimal places as you counted in Step 2.

3.2

X   5

—–

16.0   (Final product with one decimal place)

Always keep in mind that the product after multiplication must have the same number of decimal places as the factors. ## Multiplying Two Decimal Numbers

Example: Multiply 2.4 by 0.6.

Step 1: Multiply as if Whole Numbers

Treat both decimal numbers as if they were whole numbers. Multiply them just as you would with two whole numbers, ignoring the decimal points for now.

2.4

x 0.6

—–

144   (24 multiplied by 6)

Step 2: Adjust the Decimal Places

Count the number of decimal places in both decimal numbers (2.4 has one decimal place, and 0.6 has one decimal place).

The total number of decimal places in the product should be the sum of the decimal places in the original numbers (1 + 1 = 2).

Step 3: Place the Decimal Point

Place the decimal point in the product by counting from the right, starting at the end of the result. Count the number of decimal places you determined in Step 2.

2.4

x 0.6

—–

1.44   (Final product with two decimal places)

### Multiplying Decimals by 10, 100 and 1000

Multiplying decimals by powers of 10, such as 10, 100, and 1000, is a straightforward process that involves shifting the decimal point to the right by the number of positions corresponding to the number of zeros in the power of 10. Here are the rules for multiplying decimals by 10, 100, and 1000:

Example: Multiply 3.75 X 10 = 37.5

• If we multiply any decimal by 100, we shift the decimal point two places towards the right.

Example: Multiply 2.68 X 100 = 268.00 or 268

• Similarly, if we multiply a decimal by 1000, we shift the decimal point by three places towards the right, and so on.

Example: Multiply 0.43 X 1000 = 430.00 or 430 There have been times when we booked them last minute, but the teachers have been extremely well-prepared and the help desk at etutorworld is very prompt.

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Important Notes:

Here are some important notes related to the concept of multiplying decimals.

1. When multiplying decimals, always pay attention to the place value of each digit, especially when shifting the decimal point.
2. When you multiply a decimal by a power of 10 (10, 100, 1000, etc.), the decimal point shifts to the right by the same number of places as the exponent of the power of 10. This results in the value being scaled up by that power of 10.
3. When multiplying decimals, if there’s a zero to the right of the decimal point in one of the factors, you can often omit it during multiplication since it doesn’t affect the result. For example, 2.5 * 0.6 is the same as 2.5 * 6.
4. When determining the number of decimal places in the product, count the total number of decimal places in the multiplied numbers. It will tell you where the decimal point should be placed in the final answer.
5. If the product has more decimal places than the number of digits, zeros can be inserted on the left before placing the decimal point in the product.
6. The order of multiplication does not affect the result when multiplying decimals. For example, 3.2 * 4.5 is the same as 4.5 * 3.2.

## Order of Operations FAQS

#### How do you multiply decimals by whole numbers?

To multiply a decimal by a whole number, you can ignore the decimal point initially and perform the multiplication as if it were a whole number. Then, count the total decimal places in both the decimal and the whole number. Place the decimal point in the product so that it has the same number of decimal places as the sum of the decimal places in the original numbers.

#### How do you multiply decimals by decimals?

When multiplying decimals by decimals, you should first ignore the decimal points and multiply them as if they were whole numbers. Count the total decimal places in both numbers and place the decimal point in the result so that it has the same number of decimal places.

#### What is the shortcut for multiplying decimals?

One shortcut is to estimate or round the decimals to whole numbers, multiply them, and then adjust the decimal point based on the original numbers’ precision. It is useful for mental calculations.

#### What happens when you multiply a whole number by a decimal?

When you multiply a whole number by a decimal, the result will be a decimal. The number of decimal places in the product depends on the number of decimal places in the decimal you’re multiplying by.

#### Do you need to align the decimal points when multiplying decimals?

No, you don’t need to align the decimal points when multiplying decimals. You can treat them like whole numbers during the initial multiplication. However, when you place the decimal point in the final answer, it must be correctly positioned based on the rules for decimal multiplication.

#### What if the decimals have different numbers of decimal places?

Suppose the decimals you’re multiplying have different numbers of decimal places. In that case, you can adjust one or both to have the same number of decimal places before multiplying. You can add trailing zeros to achieve this.

#### Can you multiply decimals with negative numbers?

Yes, you can multiply decimals with negative numbers just like you would with positive numbers. Pay attention to the sign of the result; a negative times a positive is negative, and a negative times a negative is positive. Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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