Decimals are used to express both the whole number and the fraction. In this case, we separate the full number from the fraction by inserting a “.”, often known as a decimal point. Assume you’re going to get a cone of ice cream. The vendor informs you that ice cream costs $ 2 and 50 cents.
If you want to convey this sum in a single figure, you will state that the ice cream cone costs $2.50. There are numerous examples of real-life scenarios in which you may use decimals. With this in mind, keep reading to learn everything you need to know about decimals!
What are decimals?
Decimals are a group of integers that are written together with a dot in between them called a decimal point. When thinking about the decimal place, all numbers to the left of the point are whole numbers (i.e., units, tens, hundreds, thousands, etc.) while all numbers to the right are decimals (i.e., tenths, hundredths, thousandths).
With decimals, the place value system for the whole number component is the same as the whole number. However, after the decimal point, a new realm of numbers emerges in which we use decimal fractions to indicate the value. As we move to the left, each place digit is ten times greater than the previous place digit.
How do you divide decimals?
When dividing a decimal number by a whole number, the division is done in the same way as it is done with whole numbers. We begin by dividing the two numbers without regard for the decimal point. The decimal point in the quotient is then placed in the same position as the decimal point in the dividend. For instance, 18.2 divided by 2 equals 9.1.
You may come across having to divide two decimals. To do this, convert the decimals into whole numbers by multiplying them by 10, 100, or 1000 – depending on what is needed to form a whole number. For instance, 13.8 divided by 0.6 becomes 138 divided by 6 which equals 23.
How to change a fraction to a decimal?
Dividing decimals by whole numbers
Dividing decimals by whole numbers is similar to dividing whole numbers. Because the dividend is a decimal and the divisor is a whole number, the quotient will have the same number of decimals as the dividend. The division of decimals with a whole number is simple if you follow the following steps:
- Step 1: To divide 78.924, ignore the decimal and divide normally until you get 0 as the residual.
- Step 2: In the quotient, place the decimal point in the same location as in the dividend. 78.92/4 = 19.73 As a result, the solution is 19.73, where the decimal is inserted according to the decimal of the dividend.
Dividing decimals by another decimal number isn’t that tricky even if it seems daunting. Both the dividend and the divisor in this division are decimals so we can solve them using one of two ways. In the first technique, we first move the divisor’s decimals to make it a whole number, and then we move the dividend’s decimals. Let us break this down using the following steps:
- Step 1: To divide 48.5 by 3.5, move the divisor’s decimal to the right as many times as necessary to make it a whole number. This results in a divisor of 35.
- Step 2: Increase the decimal in the dividend by the same number of digits you increased it in the divisor. This results in the divisor 485.
- Step 3: Divide the dividend (485) by the divisor (35) as you normally would, and you should get 13.85 if you divide it fully.
When the number of digits after the decimal in the dividend is greater or less than the number of decimals in the divisor, the second technique is applied. If the decimal place of the dividend is more than or equal to the decimal place of the divisor follow these steps:
- Step 1: Ignore the decimal and divide normally until the division with remainders is 0. To divide 0.09 by 0.3, for example, we omit the digits and express it as 9 divided by 3 = 3.
- Step 2: Use the following formula to position the decimal point: Dividend’s decimal place – Divisor’s decimal place = Quotient’s decimal place. Using the formula, we now get 2-1 = 1. As a result, the decimal of the quotient will be 0.3.
If the decimal place of the dividend is less than the decimal place of the divisor, convert the decimal to a fraction. For example, 0.4/0.02 = (4/10)/(2/100) = (4/10)/(100/2) = 20.
What are terminating and repeating decimals?
Dividing decimals through long division
Dividing decimals is identical to dividing entire numbers, except that you must first manage the decimal point. Here’s a step-by-step guide to dividing decimals.
- Remember this tip: As with whole-number division, decimal division does not always work out evenly in the end. When it comes to decimals, you never write a residual. Attach enough trailing zeros to round the quotient to a specific number of decimal places. Because the digit to the right of the digit you’re rounding tells you whether to round up or down, you must always calculate the division to one extra place.
Step 1
With the divisor and dividend, move the decimal point. By shifting the decimal point all the way to the right, you can convert the divisor (the number you’re dividing by) to a whole number. Simultaneously, move the decimal point in the dividend (the number you’re dividing) to the right the equal number of places.
Step 2
Insert a decimal point in the quotient (the result of the division) right above the decimal point in the dividend. This is illustrated in our example below.
Step 3
Divide as normal, taking care to align the quotient so that the decimal point falls into position. Align each digit in the quotient with the last digit in the dividend utilized in that cycle of division.
Long Division Example
Practice Question: Divide 9.152 by 0.8
By moving the decimal point one position to the right (multiply it by 10), you can convert 0.8 to the full number 8. Simultaneously, move the decimal point in 9.1526 one position to the right. Put your decimal point right above where it falls in 91.25.
______
0.8 ) 9.152
Becomes:
______
8) 91.520
Then, continue as you usually would:
11.44
8) 91.52
8
11
8
3 5
3 2
32
32
0
As such, 0.8/9.152 is 11.44
Examples on dividing decimals
Divide 21.9 by 0.015
____
0.015) 21.9
By multiplying each side by 1000, you can turn 0.015 into 15, making it far easier to calculate.
1460
15) 21900
15
69
60
90
90
0
As such, 21.9/0.015 = 1460
Divide 9.345 by 0.05
______
0.05) 9.345
By multiplying each side by 100, you can turn 0.05 into 5, making it easier to calculate.
186.9
5) 934.5
5
43
40
34
30
45
45
0
8.342 divided by 2
As the number is already whole, we do not need to multiply it and can simply go straight into the process of long division.
4.171
2) 8.342
8
03
2
14
14
02
2
0
Need more help?
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