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# Basic Math/Curious

Question
hi there,  this is in regards to figuring out how to deal with decimals type problems.

1) I have this math problem:    0.025 /  0.0082 = 3.0487
2) the other is almost identical:   0.025 / 0.00082 = 30.48

I was wondering if u could explain to me how u correctly place the decimal in the answer of each problem please? Is there a trick in the decimal positioning process I can use to easily find out where to place the decimal?
Thank you

Hello, Dan.

When dividing by a decimal, the first step is to move the decimal point of the divisor (the number that is doing the dividing) to the right, in order to make a whole number.

For your first example, .025 / .0082, the divisor is .0082; moving the decimal point four places to the right would give you 82. However, whatever you do to the divisor must also be done to the dividend (the number that is being divided into). Thus, .025 becomes 250.

Now, you can divide, using normal rules of division: 250 / 82. First, you must ask how many times 82 divides into 250, and the answer is 3, with a remainder of 4 (82 x 3 = 246; 250-246 = 4). Bring the 0 down (since 250 can be written as 250.0000000... etc.), and then divide 82 into 40. This is 0. 82 then divided into 400 gives you 4; 82 x 4 = 328; subtracting 328 from 400 gives you 72. Drop down another 0 and divide 82 into 720. This yields 8 (82 x 8 = 656; 720 - 656 = 64). Finally, drop down another 0 and divide 82 into 640. This gives you 7 (82 x 7 = 574).

The rules are the same for .025 / .00082, except in this case, you must move the decimal point 5 places to the right. This still gives you 82 but the new dividend will be 2500. As you can plainly see, the dividend in the second example is 10 times greater than the original dividend. Therefore, the quotient will also be 10 times greater. And, of course, this is what we find: 30.487 is ten times greater than 3.0487.

I hope that this helps.

Regards,
John
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Basic Math

Volunteer

#### John Zalewski

##### Expertise

I can help you solve problems involving fractions, decimals, ratios, and algebra. I can teach you how to do math faster, and even in your head. I can teach math definitions, and help you study, if necessary. Please do not ask any graphing, trigonometry, or calculus questions. Try to work through homework questions before asking for assistance.

##### Experience

I routinely process numbers of all kinds in my head, without need of a calculator.

Education/Credentials
I was an A math student while in high school.