Multiplying and Dividing Decimals Study Guide
Introduction to Multiplying and Dividing Decimals
Can you do division? Divide a loaf by a knife—what's the answer to that?
—From Through the Looking Glass, by LEWIS CARROLL, English author and mathematician (1832–1898)
You may not have to multiply and divide decimals as often as you have to add and subtract them—though the word problems in this lesson show some practical examples of multiplication and division of decimals. However, questions on multiplying and dividing decimals often show up on tests, so it's important to know how to handle them.
To multiply decimals:
- Ignore the decimal points and multiply as you would whole numbers.
- Count the number of decimal digits (the digits to the right of the decimal point) in both of the numbers you multiplied.
- Beginning at the right side of the product (the answer), count left that number of digits, and put the decimal point to the left of the last digit you counted.
Example: 1.57 × 2.4
|1.||Multiply 157 times 24:|
|2.||Because there are a total of three decimal digits in 1.57 and 2.4, count off 3 places from the right in 3768 and place the decimal point to the left of the third digit you counted (7):|
To check the reasonableness of your work, estimate the product by using the rounding technique you learned in Lesson 6. Round each number you multiplied to the nearest whole number, and then multiply the results. If the product is close to your answer, your answer is in the ballpark. Otherwise, you may have made a mistake in placing the decimal point or in multiplying. Rounding 1.57 and 2.4 to the nearest whole numbers gives you 2 and 2. Their product is 4, which is close to your answer. Thus, your actual answer of 3.768 seems reasonable.
TipAlways think about your answers! Remember that multiplying by a decimal that has a value less than one will give you a smaller number.
In multiplying decimals, you may get a product that doesn't have enough digits for you to put in a decimal point. In that case, tack zeros onto the left of the product to give your answer enough digits; then add the decimal point.
Example: 0.03 × 0.006
|1.||Multiply 3 times 6:||3 × 6 =18|
|2.||The answer requires 5 decimal digits because there are a total of five decimal digits in 0.03 and 0.006.|
|Because there are only 2 digits in the answer (18), tack three zeros onto the left:||00018|
|3.||Put the decimal point at the front of the number (which is 5 digits in from the right):|
To quickly multiply a number by 10, just move the decimal point one digit to the right. To multiply a number by 100, move the decimal point two digits to the right. To multiply a number by 1,000, move the decimal point three digits to the right. In general, just count the number of zeros, and move the decimal point that number of digits to the right. If you don't have enough digits, first tack zeros onto the right.
Example: 1,000 × 3.82
|1.||Since there are three zeros in 1,000, move the decimal point in 3.82 three digits to the right.|
|2.||Since 3.82 has only two decimal digits to the right of the decimal point, add one zero on the right before moving the decimal point:||3.820|
Thus, 1,000 × 3.82 × 3,820
To multiply by any multiple of 10, you can ignore the last zero digits, and add them back on to your answer in the end. For example, with 220 × 3,000, think of it to start as 22 × 3 = 66. Then, add back the four zeros that were temporarily removed: 220 × 3,000 = 660,000.
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