Profile
Settings
Refer your friends
Sign out
A decimal fraction is a fraction whose denominator is 10 or a power of 10 like 100, 1000, 10000, etc. A decimal fraction is written with a decimal point and no denominator.
Example:
2/10 can be written as 0.2
42/100 can be written as 0.42
79/1000 can be written as 0.079
When you are dividing decimals, you first have to make them into whole numbers and to do that. You have to alter the place of the decimal point.
1376/100 ÷ 32/10
13.76/ 3.2
Move the decimal point all the way to the right in the divisor to make it a whole number.
3.2 → 32
Move the decimal in the dividend to the same number of places as the divisor.
13.76 →137.6
137.6/ 32
Now divide as you would normally do.
You also have to place the decimal in the quotient in the correct place. To know how to do that, let’s first understand:
How to divide decimal fractions with whole numbers?
In this case, the divisor is the whole number, and the dividend is the decimal. Let’s take an example:
Suppose you have to divide 63.42 ÷ 2.
Step 1: Divide it as you would normally do until you get the remainder 0, without paying attention to the decimal.
Step 2: Now, place the decimal in the same position as it is in the dividend.
By dividing 63.42 by 2, we get the quotient of 31.71.
As you can see, the decimal is placed before the tenth place in the quotient as it was in the dividend.
Long-form division of this would look like this:
How to divide decimals with other decimals?
In this case, both the dividend and divisor are in decimal form.
There are two ways to solve them.
First method:
Step 1: Move the decimals in the divisor to the right so as to make it a whole number.
Step 2: Move the decimals in the dividend up to the same number as you did in the divisor.
Step 3: Now divide the two numbers as you would normally do.
Let’s take an example:
37.5 ÷ 4.5
Step 1: Make the divisor a whole number, 4.5 → 45
Step 2: Move the decimal to the same number of places in the dividend, 37.5 → 375
375 ÷ 45 = 8.33
Second method:
This method is used when the number of places after the decimal in the dividend is more or less than the number of decimals in the divisor.
1st case: If the decimal place in the dividend is more than or equal to the divisor’s decimal place.
Perform the division and ignore the decimals until you get the remainder as zero.
To place the decimal in the quotient, use the formula – Dividend’s decimal place – Divisor’s decimal place = Quotient’s decimal place.
Example:
0.14 ÷ 0.7 —> 14 ÷ 7 = 2
Now, use the above mentioned formula.
2 decimal place – 1 decimal place = 1 decimal place
So, the quotient 2 will become 0.2.
2nd case: If the decimal place in the dividend is less than the decimal place is the divisor.
Convert the decimal into a fraction.
0.12 ÷ 0.004 will become
12/100 ÷ 4/1000 = 12/100 x 1000/4
= 30
Now that you have understood how division for decimal numbers works, let’s understand how division works for decimal fractions.
Decimal fractions have a denominator of 10 or a power of 10.
81.5/ 10
76.85/ 100
52.325/ 1000
Notice here that the number of zeros in the denominator is equal to the number of digits after the decimal.
Now, to divide the number, you have to shift the decimal to the left to the place equal to the number of zeros in the divisor.
Let’s take a few examples:
85.5 ÷ 10
= 855/10 ÷ 10
= 855/10 x 1/10
= 855/100
= 8.55
Therefore, 85.5 ÷ 10 = 8.55.
Here, the decimal shift is one place to the left.
752.25 ÷ 100
= 75225/ 100 ÷ 100
= 75225/ 100 x 1/100
= 75225/ 10000
= 7.5225
Here, the decimal shift is two places to the left.
Conclusion:
A decimal is any improper or proper fraction that has a denominator of 10 or a power of 10 like 100, 1000 and so on. The word decimal has the prefix “deci”, which means 0.1 or 1/10. A decimal fraction has the denominator 10, 100, etc. 23/100 as a decimal fraction, but 2/15 is a common fraction.
