How do you multiply with a decimal?
A – Multiply decimals the same way you would multiply other numbers. Then, count how many digits are after the decimal points in the multiplier and multiplicand and put the decimal point in the product that many places from the end. Ex.1.4 × 0.23 = Multiply as normal There is 1 digit after the decimal point in the multiplicand (1.4) and 2 digits after the decimal point in the multiplier (0.23). Move the decimal point in the product 3 (1 + 2) places from the end of the number: 0.322.1.4 × 0.23 = 0.322
What happens if you multiply a decimal?
How to Add, Subtract, Multiply, and Divide Mixed Numbers | Math with Mr. J
Multiplying and Dividing Decimals
- Multiplying and Dividing Decimals
- Learning Objective(s)
- · Multiply two or more decimals.
- · Multiply a decimal by a power of 10.
- · Divide by a decimal.
- · Divide a decimal by a power of 10.
- · Solve application problems that require decimal multiplication or division.
As with whole numbers, sometimes you run into situations where you need to multiply or divide decimals. And just as there is a correct way to multiply and divide whole numbers, so, too, there is a correct way to multiply and divide decimals. Imagine that a couple eats dinner at a Japanese steakhouse.
The bill for the meal is $58.32—which includes a tax of $4.64. To calculate the tip, they can double the tax. So if they know how to multiply $4.64 by 2, the couple can figure out how much they should leave for the tip. Here’s another problem. Andy just sold his van that averaged 20 miles per gallon of gasoline.
He bought a new pickup truck and took it on a trip of 614.25 miles. He used 31.5 gallons of gas to make it that far. Did Andy get better gas mileage with the new truck? Both of these problems can be solved by multiplying or dividing decimals. Here’s how to do it.
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Notice how the digits in the two solutions are exactly the same – the multiplication does not change at all. The difference lies in the placement of the decimal point in the final answers: 214 · 36 = 7,704, and 21.4 · 3.6 = 77.04.
- To find out where to put the decimal point in a decimal multiplication problem, count the total number of decimal places in each of the factors.
- 21.4 the first factor has one decimal place
- 3.6 the second factor has one decimal place
- 77.04 the product will have 1 + 1 = 2 decimal places
- Note that the decimal points do not have to be aligned as for addition and subtraction.
| Example | |||
| Problem | 3.04 · 6.1 = ? | ||
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| Answer | 3.04 · 6.1 = 18.544 |
Sometimes you may need to insert zeros in front of the product so that you have the right number of decimal places. See the final answer in the example below:
| Example | |||
| Problem | 0.037 · 0.08 = ? | ||
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Set up the problem. Multiply. | ||
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| Answer | 0.037 · 0.08 = 0.00296 | Note that you needed to add zeros before 296 to get the 5 decimal places. |
If one or more zeros occur on the right in the product, they are not dropped until after the decimal point is inserted.
| Example | |||
| Problem | 2.04 · 1.95 = ? | ||
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| Answer | 2.04 · 1.95 = 3.978 | Answer can omit the final trailing 0. |
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- Multiplying Decimals
- To multiply decimals:
- · Set up and multiply the numbers as you do with whole numbers.
- · Count the total number of decimal places in both of the factors.
- · Place the decimal point in the product so that the number of decimal places in the product is the sum of the decimal places in the factors.
· Keep all zeros in the product when you place the decimal point. You can drop the zeros on the right once the decimal point has been placed in the product. If the number of decimal places is greater than the number of digits in the product, you can insert zeros in front of the product.
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- A) 15769.6
- B) 1576.96
- C) 157.696
- D) 15.7696
A) 15769.6 Incorrect. Pay attention to the placement of the decimal point. The correct answer is 157.696. B) 1576.96 Incorrect. Pay attention to the placement of the decimal point. The correct answer is 157.696. C) 157.696 Correct. To find the product, multiply 512 · 308 = 157696. Count the total number of decimal places in the factors, 3, and then place a decimal point in the product so that the product has three decimal places as well. The answer is 157.696. D) 15.7696 Incorrect. Pay attention to the placement of the decimal point. The correct answer is 157.696.
Take a moment to multiply 4.469 by 10. Now do 4.469 · 100. Finally, do 4.469 · 1,000. Notice any patterns in your products?
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Notice that the products keep getting greater by one place value as the multiplier (10, 100, and 1,000) increases. In fact, the decimal point moves to the right by the same number of zeros in the power of ten multiplier.
| 4.469 · 10 = 44,69 ^ | 4.469 · 100 = 446,9 ^ | 4.469 · 1,000 = 4469, ^ |
You can use this observation to help you quickly multiply any decimal by a power of ten (10, 100, 1,000, etc).
| Example | |||
| Problem | 0.03 · 100 = ? | ||
| 0.03 · 1 00 = ? | 100 has two zeros. | ||
| 0.03 · 100 = 3 | Move the decimal point two places to the right to find the product. | ||
| Answer | 0.03 · 100 = 3 |
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To divide decimals, you will once again apply the methods you use for dividing whole numbers. Look at the two problems below. How are the methods similar? Notice that the division occurs in the same way—the only difference is the placement of the decimal point in the,
| Example | |||
| Problem | 18.32 ÷ 8 = ? | ||
| _ 8 ) 1 8.3 2 | Set up the problem. | ||
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Divide. | ||
| 2.2 9 8 ) 1 8.3 2 | Place decimal point in the quotient. It should be placed directly above the decimal point in the dividend. | ||
| Answer | 18.32 ÷ 8 = 2.29 |
But what about a case where you are dividing by a decimal, as in the problem below? In cases like this, you can use powers of 10 to help create an easier problem to solve. In this case, you can multiply the, 0.3, by 10 to move the decimal point 1 place to the right.
| Example | |||
| Problem | 260.1 ÷ 0.3 = ? | ||
| _ 0.3 ) 2 6 0.1 | Set up the problem. | ||
| _ 3,) 2 6 0 1, | Multiply divisor and dividend by 10 to create a whole number divisor. | ||
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Divide. | ||
| Answer | 260.1 ÷ 0.3 = 867 |
Often, the dividend will still be a decimal after multiplying by a power of 10. In this case, the placement of the decimal point must align with the decimal point in the dividend.
| Example | |||
| Problem | 15.275 ÷ 3.25 = ? | ||
| _ 3.2 5 ) 1 5.2 7 5 | Set up the problem. | ||
| _ 3 2 5,) 1 5 2 7,5 | Multiply divisor and dividend by 100 to create a whole number divisor. | ||
4.7 3 2 5,) 1 5 2 7,5
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Divide.325 goes into 1527 four times, so the number 4 is placed above the digit 7. The decimal point in the quotient is placed directly above the decimal point in the dividend. | ||
| Answer | 15.275 ÷ 3.25 = 4.7 |
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- A) 5,019
- B) 501.9
- C) 50.19
- D) 0.5019
A) 5,019 Incorrect. Multiply both the divisor and the dividend by 10 (this will change 0.5 into a whole number), and then divide. Then place the decimal point in the quotient directly over the decimal point in the dividend. The correct answer is 50.19. B) 501.9 Incorrect. Multiply both the divisor and the dividend by 10 (this will change 0.5 into a whole number), and then divide. Then place the decimal point in the quotient directly over the decimal point in the dividend. The correct answer is 50.19. C) 50.19 Correct. This problem can be set up as 250.95 ÷ 5; the quotient is 50.19. D) 0.5019 Incorrect. Remember that when you divide, you do not count the total number of decimal places in the divisor and dividend. You change the divisor to a whole number, then move the decimal point in the dividend the same number of places and divide. Finally, place the decimal point in the quotient directly over the decimal point in the dividend. The correct answer is 50.19.
Recall that when you multiply a decimal by a power of ten (10, 100, 1,000, etc), the placement of the decimal point in the product will move to the right according to the number of zeros in the power of ten. For instance, 4.12 · 10 = 41.2. Multiplication and division are inverse operations, so you can expect that if you divide a decimal by a power of ten, the decimal point in the quotient will also correspond to the number of zeros in the power of ten. In the examples above, notice that each quotient still contains the digits 4469—but as another 0 is added to the end of each power of ten in the divisor, the decimal point moves an additional place to the left in the quotient.
| Dividing by Powers of Ten To divide a decimal by a power of ten (10, 100, 1,000, etc.), count the number of zeros in the divisor. Then move the decimal point in the dividend that number of decimal places to the left; this will be your quotient. |
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- A) 0.00045
- B) 0.045
- C) 4.5
- D) 4,500
A) 0.00045 Correct. There are two zeros in the divisor (100), so to find the quotient, take the dividend (0.045) and move the decimal point two places to the left. The quotient is 0.00045. B) 0.045 Incorrect.0.045 is the dividend in the problem; it cannot be the quotient unless the divisor is 1. The correct answer is 0.00045. C) 4.5 Incorrect.4.5 would be the correct answer if you multiplied 0.045 by 100, not divided it by 100. The correct answer is 0.00045. D) 4,500 Incorrect.4,500 would be the correct answer if you multiplied 0.045 by 100,000, not divided it by 100. The correct answer is 0.00045.
Solving Problems by Multiplying or Dividing Decimals Now let’s return to the two problems from the beginning of this section. You know how to multiply and divide with decimals now. Let’s put that knowledge to the test.
| Example | |||
| Problem | A couple eats dinner at a Japanese steakhouse. The bill for the meal totals $58.32—which includes a tax of $4.64. To calculate the tip, they can double the tax. How much tip should the couple leave? | ||
| 4.64 x 2 | Set up a multiplication problem. | ||
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Multiply. | ||
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Count the number of decimal places in the two factors, and place the decimal point accordingly. | ||
| Answer | The couple should leave a tip of $9.28. |
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- -3 1 5
- 2 9 9 2
- -2 8 3 5
- 1 5 7 5
- -1 5 7 5
- 0
Learning to multiply and divide with decimals is an important skill. In both cases, you work with the decimals as you have worked with whole numbers, but you have to figure out where the decimal point goes. When multiplying decimals, the number of decimal places in the product is the sum of the decimal places in the factors.
What is 0.3 multiplying 1000?
Multiply 0.3 and 1000 to get 300.
How do you multiply 0.2 10?
Multiply 0.2 and 10 to get 2.
Is 0.6 and 0.60 and 0.600 equal?
0.6 is equal to 0.60, as the extra 0 in 0.60 does not change the value of the number. Both represent the same fraction of a whole (6/10 = 60/100).
What are common mistakes when multiplying decimals?
Multiplying Decimals To multiplying decimals, just ignore the decimal and multiply like normal. Then re-insert the decimal in the correct spot.1. Multiply the numbers just as if they were whole numbers. (do not align the decimal points) 2. Place the decimal a.
| Example: | $34.5∗20.5$ |
| $345∗205=70725$ | |
| Think: | $20$ times $35$ would be $700$. |
| The answer should be around 700: | $34.5∗20.5=707.25$ |
b. Counting Decimal Places method: • Count the decimal places to the right of the decimal points in each of the original numbers. • Then put the decimal point in the answer – it will have as many decimal places as the two original numbers combined. • Start at the right-most digit of the product. Move the decimal point to the left the necessary number of decimal places.
| Example: | $3.4∗0.78$ |
| $34∗78=2652$ | |
| Think: There is 1 decimal place in | 3.4. |
| There are 2 decimal places in | 0.78 |
| $1+2=3$ | |
| So there are 3 decimal places in the product. | |
| So count over from the right to get | $3.4*0.78=2.652$ |
Some times you need to add zeros to the left of the number:
| Example: | $0.03 ∗ 1.1$ | (total of 3 decimal places in the product) |
| $3 ∗ 11 = 33$ | ||
| $0.03 ∗ 1.1 = 0.033$ |
Multiplying Decimals
How do you multiply hard decimals?
Learn to multiply decimals easily by treating them as whole numbers first. Multiply the numbers without decimals, then count the total decimal places in both original numbers. Add the same number of decimal places to the product, and you’ll get the correct answer for the decimal multiplication.
How do you multiply decimals by whole numbers math is fun?
How to Multiply Decimals – Just follow these steps:
Multiply normally, ignoring the decimal points. Then put the decimal point in the answer – it will have as many decimal places as the two original numbers combined.
In other words, just count up how many numbers are after the decimal point in both numbers you are multiplying, then the answer should have that many numbers after its decimal point.