How to Divide Decimals
Introduction
Decimals are special kinds of numbers that have a whole number part and a fractional part separated by a dot called a decimal point. This decimal point is super important because it tells us where the whole number ends and the fraction begins. The digits after the decimal point have a value less than `1`. Like whole numbers, we can apply all types of math operations with decimals like add, subtract, multiply, and divide decimals.
Knowing how to divide decimals can be helpful in various real-life situations. For example, you want to organize a party and would like to have some return gifts ready for the event. You would need `14.85` inch long ribbon to tie one gift. However, the local store only sells rolls of ribbons that are `100` inches long. The ability to divide decimals would help you calculate how many pieces of ribbon you can cut out of the roll.
How to Divide Decimals?
Dividing decimals is similar to dividing whole numbers. However, there are a few different scenarios when it comes to dividing decimals:
`1`. Dividing Decimals by Whole Numbers:
This is when you have a decimal number and you're dividing it by a whole number, like `5.6` divided by `2`.
`2`. Division of a Decimal Number by Another Decimal Number:
At times you'll have one decimal number and you're dividing it by another decimal number, like `8.75` divided by `0.25`.
`3`. Division of Decimals by `10, 100,` and `1000`:
This one's pretty straightforward. You're dividing a decimal number by powers of `10`, like dividing `3.2` by `10` or `6.75` by `100`.
Each case has its own little rules to follow, but at the end of the day, it's all about figuring out where that decimal point should go!
Dividing Decimals with Whole Numbers - Long Division
For dividing decimals with whole numbers, we generally use long division and it's pretty straightforward. Here's how to do it:
`1`. Write it out:
Start by writing your division problem, like `187.2 ÷ 6`, in the long division format.
`2`. Place the decimal point:
Put your decimal point in the quotient right above the decimal point in the dividend. Then bring down the next digit.
`3`. Keep dividing:
Divide and bring down digits until you have no more digits to bring down. Make sure to keep your decimal points lined up.
Let's try an example: `187.2 ÷ 6 = 31.2`. Here, `187.2` is the dividend, `6` is the divisor, and `31.2` is the quotient.
Dividing Decimal by Another Decimal Number
How to divide decimals by decimals? When we divide decimals by another decimal, we first need to make the divisor a whole number. This involves moving the decimal point to the right. Then, we do the same for the dividend, moving its decimal point to match. After this adjustment, we perform regular long division as usual. Let's take an example to show dividing by decimals:
Example:
Divide `32.76 ÷ 0.6`.
Solution:
Given: Divisor `= 0.6` and Dividend `= 32.76`
`1`. Adjust the Divisor:
Convert `0.6` to a whole number by shifting its decimal point one place to the right. So, `0.6` becomes `6`.
`2`. Adjust the Dividend:
Move the decimal point in the dividend to the same number of places as in the divisor. Thus, `32.76` becomes `327.6`.
`3`. Perform Division:
Divide the adjusted dividend by the whole number of the divisor. In this case, `327.6 ÷ 6 = 54.6`.
Hence `32.76 ÷ 0.6 = 54.6`.
Dividing Decimals by Multiples of `10`
When we divide a decimal number by multiples of `10`, we're essentially shifting the decimal point to the left in the quotient. Let's illustrate this with an example:
Let’s observe `86.4 ÷ 10 = 8.64`. Here, notice that the digits `8, 6,` and `4` remain the same in both the original number and the quotient. However, the decimal point has shifted to the left by one place in the quotient compared to the original number.
So, in the division of decimals by `10, 100,1000,` etc the digits in the number and the quotient remain unchanged. However, the decimal point in the quotient shifts to the left by the same number of places as the number of zeros in the divisor. For instance, dividing by `10` moves the decimal point one place to the left, dividing by `100` moves it two places, dividing by `1000` moves it three places to the left, and so on.
Solved Examples
Example `1`: Calculate: ` 15.64 \div 8 `.
Solution:
We can use long division to calculate ` 15.64 \div 8 `.
` 15.64 \div 8 = 1.955 `
Please note that we brought down an extra `0` in the last step to complete the division problem. We can do this because `15.640` is the same as `15.64`.
Example `2`: Determine: ` 392.5 \div 100 `.
Solution:
When we divide ` 392.5 ` by ` 100 `, the decimal point shifts two places to the left:
` 392.5 \div 100 = 3.925 `
Example `3`: Find: ` 15.75 \div 3.5 `.
Solution:
We can use the method of long division with decimals as illustrated below.
`1`. Adjust the Divisor:
Convert `3.5` to a whole number by shifting its decimal point one place to the right. So, `3.5` becomes `35`.
`2`. Adjust the Dividend:
Move the decimal point in the dividend to the same number of places as in the divisor. Thus, `15.75` becomes `157.5`.
`3`. Perform Division:
Divide the adjusted dividend by the whole number of the divisor. In this case, `157.5 ÷ 35 = 4.5`.
Hence, ` 15.75 \div 3.5 = 4.5`.
Example `4`: If Mary bought a `3.75` meter long fabric and wants to cut it into pieces of `0.25` meters each, how many pieces can she get?
Solution:
To find the number of pieces, divide the length of the fabric by the length of each piece:
` 3.75 \div 0.25 = 15 `
So, Mary can get ` 15 ` pieces of fabric.
Example `5`. For a science experiment, Mrs. Bertin needs to equally distribute a magnesium ribbon among `6` students. If the ribbon is `37.8` `\text{cm}` long, what is the length of the ribbon each student gets in centimeters?
Solution:
To find out how much ribbon each student will get, divide the total length of the magnesium ribbon by the number of students:
` 37.8 \div 6 = 6.3 `
So, each student will get `6.3` `\text{cm}` of ribbon.
Practice Problems
Q`1`. Divide ` 48.9 ` by ` 5 `.
- ` 9.78 `
- ` 9.79 `
- ` 9.8 `
- ` 9.81 `
Answer: a
Q`2`. Find ` 382.8 ` divided by ` 23.2 `.
- ` 14.95 `
- ` 16.5 `
- ` 15.85 `
- ` 14.5 `
Answer: b
Q`3`. What is ` 567.3 ` divided by ` 1000 `?
- ` 0.5673 `
- ` 5.673 `
- ` 0.567 `
- ` 0.56730 `
Answer: a
Q`4`. If a rope measuring ` 15.6 ` `\text{meters}` is cut into ` 4 ` equal pieces, how long is each piece?
- ` 3.8 ` `\text{meters}`
- ` 3.95 ` `\text{meters}`
- ` 3.85 ` `\text{meters}`
- ` 3.9 ` `\text{meters}`
Answer: d
Q`5`. A jug contains ` 3.24 ` liters of juice. If each glass can hold ` 0.18 ` liter of juice, how many glasses can be filled from the jug?
- ` 18 `
- ` 19 `
- ` 20 `
- ` 21 `
Answer: a
Frequently Asked Questions
Q`1`. How do you divide decimals?
Answer: To divide decimals, you follow the same steps as dividing whole numbers, but you have to be careful with the placement of the decimal point. First, perform the division as if the numbers were whole numbers. Then, adjust the decimal point in the quotient to match its placement in the dividend.
Q`2`. What happens to the decimal point when dividing decimals?
Answer: When dividing decimals, the decimal point moves in the quotient to match its position in the dividend. If you move the decimal point one place to the right in the divisor, you must also move it one place to the right in the dividend.
Q`3`. Can you divide a decimal by a whole number?
Answer: Yes, you can divide a decimal by a whole number. The process is similar to dividing whole numbers, but you must be mindful of the decimal point's position in both the dividend and divisor when determining the placement of the decimal point in the quotient.
Q`4`. How do you divide a decimal by powers of `10`?
Answer: Dividing a decimal by powers of `10` is simple. To divide by `10`, move the decimal point one place to the left. To divide by `100`, move it two places to the left. For division by `1000`, move it three places to the left, and so on.
Q`5`. Can we find examples of dividing decimals in real-life situations?
Answer: Sure! Dividing decimals often comes up in real-life scenarios such as splitting bills at a restaurant, dividing ingredients in a recipe, or calculating distances traveled per unit of time. These situations require dividing quantities that are not always whole numbers, making decimal division essential for accurate calculations.