The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Why do decimal places "move" when multiplying or dividing decimals? Ask Question. Asked 4 years, 3 months ago. Active 3 years, 7 months ago. Viewed 9k times. AldenB AldenB 31 2 2 silver badges 5 5 bronze badges.
Write both numbers this way, then multiply across. Dividing by the resulting denominator in this case exactly amounts to moving the decimal point left. Add a comment. Active Oldest Votes. Now, we divide by Since it's division, we move the digits to the right. And, because has two zeros, we move each digit two spaces to the right. If you're familiar with scientific notation , we could also write this as.
Although this explanation focuses on 10 and , we can do larger powers of 10 too. For instance, multiplying. It also puts the 6 in the thousands place. Finally, the 3 goes in the hundreds place. Since we have some gaps we just fill them with zeros.
The result is. This result is a whole number. That means we don't write any digits after the decimal point. In fact, we don't even have to write the decimal point! It's invisible, right after the last zero. When you multiply a decimal by a power of 10, simply move the decimal place to the right as many places as there are 0s in the power of When you divide a decimal by a power of 10, simply move the decimal place to the left as many places as there are 0s in the power of If you multiply a decimal by 10, the decimal point will move one place to the right.
If you divide a decimal by 10, the decimal point will move one place to the left. We must first note that Next, the multiple of ten is , which has two zeros. Therefore, we move the decimal place in For instance, 4. 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.
The difference is that the decimal point moves to the right when you multiply; it moves to the left when you divide. In the examples above, notice that each quotient still contains the digits —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, , 1,, etc. Then move the decimal point in the dividend that number of decimal places to the left; this will be your quotient. Move the decimal point one place to the left in the dividend; this is the quotient.
There are two zeros in the divisor , so to find the quotient, take the dividend 0. The quotient is 0. The correct answer is 0. Solving Problems by Multiplying or Dividing Decimals. You know how to multiply and divide with decimals now. A couple eats dinner at a Japanese steakhouse. How much tip should the couple leave? Set up a multiplication problem. Count the number of decimal places in the two factors, and place the decimal point accordingly.
Set up a division problem. Make the divisor a whole number by multiplying by 10; do the same to the dividend. Insert a decimal point in the quotient so that it is directly above the decimal point in the dividend. Andy gets He used to get 20 miles per gallon.
He does not get better gas mileage with the new truck. 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.
When dividing by decimals, move the decimal point in the dividend the same number of places to the right as you move the decimal point in the divisor. Then place the decimal point in the quotient above the decimal point in the dividend. Example Problem 3. Answer 3. Example Problem 0.
Answer 0. Example Problem 2. Answer 2. B C Example Problem Answer D 4, Incorrect. Example Problem A couple eats dinner at a Japanese steakhouse. Example Problem Andy just sold his van that averaged 20 miles per gallon of gasoline.
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