Decimal Division? I know the answer for "3.6 / 0.04" is "90", but how?

helpimstuck

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Decimal Division? I know the answer for "3.6 / 0.04" is "90", but how?

Hi there, so I'm doing a practice test because I want to brush up on math since its been awhile and I came across something I dont even know what it is or called and how to get the answer.
I'm allowed a calculator for the test which is fine and I can get the answer but I want to know what the process is called and how to go about getting the answer, here's the problem, with a multi-choice to choose from.

Q. 3.6 / 0.04

144
9
14.4
90
180

I know the answer is 90 but how? And what is this even called. Decimal division? The prep test shows the explanation...

3.6 / 0.04
= 36 / 0.4
= 360 / 4
= 90

Here, I know we can move the decimal 1 place to the right for both sides, but then where does the 0 come from in (360). I think to make the .4 a whole number you must times both sides by 10 because the 4 is in the tenths after the decimal?
Thanks for any help in advance. :)
 
You need to multiply both the top (numerator) and the bottom (denominator) by 100, to get two Whole numbers.

\(\displaystyle \dfrac{3.6}{0.04} \times \dfrac{100}{100} = \dfrac{360}{4}\)

Every time we multiply a decimal number by 10, the decimal point shifts one position to the right.

3.6 × 10 = 36.

3.6 × 10 × 10 = 360.

3.6 × 10 × 10 × 10 = 3600.

Do you know? 100/100 is 1. Anytime the numerator and denominator match, the value of the ratio is 1 (no zeros, of course). We don't change the value of anything, when we multiply by forms of 1, so we're free to do that anytime it helps. Above, 3.6/0.04 is multiplied by 1, and the result 360/4 is an equivalent ratio.

When we divide by a decimal number longhand, we want the divisor to be a Whole number. We examine the position of its decimal point, to determine how many positions to the right we need to shift. Then we shift the same number of places in both the divisor and dividend. (This is equivalent to multiplying each by 10s). The divisor becomes Whole (the dividend may not be), and the decimal point's new position in the dividend sets the position in the quotient (aligned directly above the dividend ). After that, we ignore decimal points and divide by hand as usual; multiplying dividend and divisor by a form of 1 allows this. (Note: Some countries format and complete longhand division differently). :cool:
 
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… And what is this even called. Decimal division? …
Sure, why not. :cool:

If you were doing it by hand, it would be called long-hand decimal division.

The step where we shift decimal points in the divisor and dividend, before long-hand division, maybe has no name. Shifting decimals points are used elsewhere, too, like working with scientific notation (where we multiply or divide very big or very small decimal numbers by powers of 10) -- stuff you'll learn about later, if you haven't already.
 
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3.6 / 0.04
= 36 / 0.4
= 360 / 4
= 90

Here, I know we can move the decimal 1 place to the right for both sides, but then where does the 0 come from in (360). I think to make the .4 a whole number you must times both sides by 10 because the 4 is in the tenths after the decimal?
Thanks for any help in advance. :)
Yes, "moving the decimal point" is just "slang" for "multiply both sides by 10" or "divide both sides by 10. To convert 0.4 to an whole number, multiply by 10. Of course, if you multiply or divide the denominator of a fraction by something you must also multiply or divide the numerator by the same thing to keep the fraction constant. You multiply 0.4 by 10 so you must multiply 36 by 10 to get 360.

(And you "multiply" numbers- you do NOT "times" them!)
 
To build a little on the excellent answers already provided,

\(\displaystyle \text {For any number } a, \text { it is true that } a = a \times 1.\)

If you want to sound fancy, you can say that 1 is the multiplicative identity element, which simply means that when you multiply by a given number times 1, the product is that same given number.

\(\displaystyle \text {For any number } b \text { except } 0, \text {it is true that } 1 = \dfrac{b}{b}.\)

It is a standard technique in math to change a number or expression in a form that is hard to deal with into a more convenient equivalent form. So you will find quite a few places where we go

\(\displaystyle a = a \times 1 = a \times \dfrac{b}{b} = c\)

to change some quantity expressed in form a into one that is easier to deal with, namely c, which is the same quantity expressed in a different form.

The trick is figuring out what b is appropriate for the specific problem.

In this case, the number with the most meaningful figures to the right of the decimal point is 0.04, with 2 meaningful figures. But

\(\displaystyle 0.04 = \dfrac{4}{100}\)

so we could get rid of all the decimals by multiplying by 100. So b = 100 for this problem. But we have to multiply by b / b = 1.

\(\displaystyle \dfrac{3.6}{0.04} = \dfrac{3.6}{0.04} \times 1 = \dfrac{3.6}{0.04} \times \dfrac{100}{100} = \dfrac{360}{4}.\)

If you were working with numbers the longest of which had three meaningful numbers to the right of the decimal point, b would be 1000 and you would multiply by

\(\displaystyle \dfrac{1000}{1000}.\)

In different problems b and so b / b will differ, but the general technique will be the same.
 
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Hi there, so I'm doing a practice test because I want to brush up on math since its been awhile and I came across something I dont even know what it is or called and how to get the answer.
I'm allowed a calculator for the test which is fine and I can get the answer but I want to know what the process is called and how to go about getting the answer, here's the problem, with a multi-choice to choose from.

Q. 3.6 / 0.04

144
9
14.4
90
180

I know the answer is 90 but how? And what is this even called. Decimal division? The prep test shows the explanation...

3.6 / 0.04
= 36 / 0.4
= 360 / 4
= 90

Here, I know we can move the decimal 1 place to the right for both sides, but then where does the 0 come from in (360). I think to make the .4 a whole number you must times both sides by 10 because the 4 is in the tenths after the decimal?
Thanks for any help in advance. :)

hoping to help what has already been written;
if you were to divide 3.6 by .04, long division, you move the decimal pt two places to the right in both terms. Then you are dividing 360 by 4, and get 90 as the answer.
 
Thanks to everyone! :)

I truly appreciate the help, all great information. Will be practicing this process till I'm competent.
I have another question regarding another problem I'm having should I post here or make a new thread?

Thanks again!
 
Hi there, so I'm doing a practice test because I want to brush up on math since its been awhile and I came across something I dont even know what it is or called and how to get the answer.
I'm allowed a calculator for the test which is fine and I can get the answer but I want to know what the process is called and how to go about getting the answer, here's the problem, with a multi-choice to choose from.

Q. 3.6 / 0.04

144
9
14.4
90
180

I know the answer is 90 but how? And what is this even called. Decimal division? The prep test shows the explanation...

3.6 / 0.04
= 36 / 0.4
= 360 / 4
= 90

Here, I know we can move the decimal 1 place to the right for both sides, but then where does the 0 come from in (360). I think to make the .4 a whole number you must times both sides by 10 because the 4 is in the tenths after the decimal?
Thanks for any help in advance. :)
You should try to understand the problem, that way you do not even have to do the division! You want to know how many times .04 (Think 4 cents!) goes into 3.6 or 3.60 (think $3.60). That is you want to know how many 4 cent items you can buy with $3.60. Well you can buy 25 of these 4 cents items for a dollar. So you simple compute (actually estimate) 25*3.6. Well 25*3=75 and 25*4=100, so the answer is between 75 and 100. The only sensible choice is 90 and I never did any long division.

Ofcourse you could have moved the decimals for 3.6/.04and get 360/4 which is easily seen to be 90.
 
Hey, there have been so many good answers and great ways of reaching it too- it also aconversion you can check out.
 
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