How to Solve Decimal Fraction Problems Step by Step
To recall we know that a Fraction is formed up of two parts - Numerator and Denominator.
And expressed as - Numerator/Denominator.
A Fraction or a Mixed Number in which the Denominator is a power of 10 such as 10, 100, 1000. etc. usually expressed by use of the Decimal point is termed as Decimal Fraction Math. Writing the Fraction in terms of Decimal makes it easier to carry on Mathematical Operations on them. For example any Fraction which has a Denominator as power of 10 like 53/100 can be written in Decimal as 0.53.
Examples of Decimal Fractions
4/100 = 0.04
57/10 = 5.7
53/100 = 0.53
The Right Way to Study about Decimals
Read the entire Number part first, followed by "and," and then read the Fractional component in the same way as Whole Numbers, but with the last digit's place value. Individual digits are always read as a Decimal Number. A Decimal Number of 145.367, for example, might be interpreted as one hundred forty-five point three six seven.
What is Decimal Fraction?
A Fraction where the Denominator i.e the bottom Number is a power of 10 such as 10, 100, 1000, etc is called a Decimal Fraction. You can write Decimal Fractions with a Decimal point and no Denominator, which make it easier to do calculations like addition, subtraction, division, and multiplication on Fractions.
Some of the Decimal Fractions examples are
1/10 th = read as one-tenth = written as 0.1 in Decimals.
6/1000 th = read as six-thousandths = written as 0.006 in Decimals
Operations on Decimal Fractions:
Addition and Subtraction of Decimal Fractions:
The given Numbers are so placed under each other that the Decimal points lie in one column below one another. The Numbers are now added or subtracted in the regular way.
For example: add 0.007 and 3.002
0. 0 0 0 7
+ 3. 0 0 0 2
____________________
3. 0 0 0 9
Multiplication of a Decimal Fraction:
When a Decimal Fraction is multiplied by the powers of 10, shift the Decimal point to the right by as many places as is the power of 10.
For example, 5.9632 x 1000 = 5963.2;
0.073 x 1000 = 730.
Multiply the given Numbers without a Decimal point. Now, in the product, the Decimal point is marked as many places of Decimal as is the sum of the Number of Decimal places in the given Numbers.
For example: we have to find the product 0.2 x 0.02 x 0.0002
Consider the Number without Decimal points
Now, 2 x 2 x 2 = 8.
Sum of Decimal places = (1 + 2 + 4) = 7.
Thus mark the Decimal point 7 places to the left that will be 0.0000008
.2 x .02 x .002 = .0000008
Dividing a Decimal Fraction By a Counting Number:
Divide the given Number without the Decimal point, by the given Number. Now, in the quotient, mark the Decimal point as many places of Decimal as there are in the dividend.
For Example we have to find the quotient for 0.0204 ÷ 17
Now, 204 ÷ 17 = 12.
Dividend contains 4 places of Decimal.
So, 0.0204 ÷ 17 = 0.0012
Dividing a Decimal Fraction By a Decimal Fraction:
Multiply both the dividend and the divisor by a suitable power of 10 to make the divisor a whole Number.
Now, proceed as above.
How to convert Decimal to Fraction
You can convert a Decimal to a Fraction by following these three steps.
Let us convert 0.25 in Fraction
Step 1: Rewrite the Decimal Number over one as a Fraction where the Decimal Number is the Numerator and the Denominator is one.
0.25/1
Step 2: Multiply both the Numerator and the Denominator by 10 to the power of the Number of digits after the Decimal point. If there is one value after the Decimal point, multiply by 10, if there are two values after the Decimal point then multiply by 100, if there are three values after the Decimal point then multiply by 1,000, and so on.
For converting 0.25 to a Fraction, there are two digits after the Decimal point. Since 10 to the 2nd power is 100, we have to multiply both the Numerator and Denominator by 100 in step two.
0.25/1 x 100/100 = 25/100
Step 3: Express the Fraction in Decimal Fraction form and simplest form.
25/100 = ¼
By following these steps in the above Decimal Fraction questions, you can conclude that the Decimal 0.25, when converted to a Fraction, is equal to 1/4.
Let us solve Decimal questions.
Solved Examples
Decimal Fractions questions
Convert the given fractions into decimal fractions:
½
Solution: ½ x 5/5
= 5/10
= 0.5
10 ¼
Solution: 10 ¼
= 10 ¼ x 25/25
= 10 (25/100)
= 10.2
Quiz Time
1. Jim purchased 100 apples from a local fruit dealer, only to discover that five of them were rotting. Can you calculate the Fraction and Decimals of the rotten apples in relation to the total apples purchased by Jim?
Ans: Out of 100 apples, we have 5 rotten ones. As a result, the Percentage of rotten oranges is 5/100. Now we must convert this Fraction to a Decimal. We must divide the Numerator 5 by the Denominator 100 to achieve this. As a result, by adding two Decimal places to the Fraction 5/100, it can be converted to a Decimal. 0.05 is the Decimal answer. As a result, the rotten apples are 0.05 in Decimals.
2. In an 80-student class, 48 pupils chose ice cream as a snack, while the other students preferred soft drinks. Calculate the Percentage of students that choose a soft drink and give the result in Decimals.
Ans: There are 80 pupils in a class, 48 students who enjoy ice cream, and 80 - 48 = 32 students who enjoy soft drinks. Soft drinks are enjoyed by 32 percent of students out of 80. This Fraction is equivalent to 2/5 on simplification. Let's convert this Fraction to a Decimal and then to a Percentage. To convert the Fraction to a Decimal, divide 2 by 5, and the result is 0.4. In order to convert 0.4 to a Percentage, we must multiply it by 100, which is 0.4 x 100 percent = 40%. As a result, the Percentage of students who enjoy soft drinks is 40%, and the Decimal equivalent is 0.4.
3. Write 1/4th in Decimals.
Ans: Let's look at how to express 1/4 in Decimals. To get a 100 in the Denominator, multiply the Numerator and Denominator with a 25. We also need to convert this Fraction to a Decimal with a Denominator of 100.
0.25 = 1/4 x 25/25 = 25/100
FAQs on Decimal Fraction Explained: Concepts, Operations & Examples
1. What is a decimal fraction?
A decimal fraction is a specific type of fraction where the denominator (the bottom number) is a power of 10, such as 10, 100, 1000, and so on. These are easily expressed using a decimal point. For example, the fraction 7/10 is written as the decimal 0.7, and 23/100 is written as 0.23.
2. How do you convert a common fraction into a decimal?
To convert a common fraction into a decimal, you simply divide the numerator (the top number) by the denominator (the bottom number). For instance, to convert the fraction 3/4 into a decimal, you would perform the division 3 ÷ 4, which equals 0.75.
3. How can a decimal number be converted back into a fraction?
To convert a decimal to a fraction, follow these steps:
- Write the decimal digits as the numerator without the decimal point.
- The denominator is 1 followed by as many zeros as there are digits after the decimal point.
- Simplify the fraction to its lowest terms.
4. What is the difference between a decimal fraction and a common fraction?
The key difference lies in the denominator. A common fraction (or vulgar fraction) can have any whole number as its denominator, like 2/3 or 5/8. In contrast, a decimal fraction specifically has a denominator that is a power of 10 (e.g., 10, 100, 1000). While all decimal fractions can be written as common fractions, not all common fractions are written as decimal fractions without becoming repeating decimals (like 1/3).
5. Why is understanding place value crucial when working with decimals?
Understanding place value is essential because it determines the value of each digit in a decimal number. Each position to the right of the decimal point represents a fraction of a whole (tenths, hundredths, thousandths, etc.). For example, in the number 12.35, the '3' represents three-tenths (3/10), while the '5' represents five-hundredths (5/100). Misinterpreting these values can lead to significant errors in calculations, measurements, and comparisons.
6. What are recurring or repeating decimals?
A recurring decimal, also known as a repeating decimal, is a decimal number in which a digit or a sequence of digits repeats forever. This occurs when converting a fraction whose denominator has prime factors other than 2 and 5. For example, 1/3 becomes 0.333..., which is written as 0.3̅. Similarly, 22/7 becomes 3.142857142857..., written as 3.1̅4̅2̅8̅5̅7̅.
7. How does multiplying or dividing a decimal by 10, 100, or 1000 affect the decimal point?
Multiplying or dividing by powers of 10 is a simple process of shifting the decimal point:
- When multiplying by 10, 100, or 1000, you move the decimal point to the right by the same number of places as there are zeros in the multiplier. For example, 4.567 x 100 = 456.7.
- When dividing by 10, 100, or 1000, you move the decimal point to the left by the same number of places. For example, 456.7 ÷ 100 = 4.567.
8. How are decimals and decimal fractions used in real-world situations?
Decimals are fundamental to many everyday activities and professional fields. Key examples include:
- Finance and Money: Prices, bank balances, and interest rates (e.g., ₹125.50, 6.5% interest).
- Measurement: Expressing weight (e.g., 55.5 kg), length (e.g., 1.75 m), and volume (e.g., 2.5 litres).
- Science and Engineering: For precise calculations, temperature readings (e.g., 37.5°C), and technical specifications.
- Sports: Recording race times (e.g., 9.58 seconds) or judging scores.
9. How do you correctly compare two decimal numbers, for example, 5.8 and 5.18?
To compare decimals correctly, follow a place-value approach from left to right:
1. First, compare the whole number parts. In this case, both numbers have a '5' as the whole number part, so they are equal.
2. Next, compare the digits in the tenths place (the first digit after the decimal). In 5.8, the digit is '8'. In 5.18, it is '1'.
3. Since 8 is greater than 1, we can conclude that 5.8 is greater than 5.18, regardless of the digits that follow.
10. What is the process for rounding off decimals to a specific number of places?
To round a decimal, identify the digit at the place you are rounding to. Then, look at the very next digit to its right.
- If this next digit is 5 or greater (5, 6, 7, 8, or 9), you round up by adding one to your target digit.
- If this next digit is 4 or less (0, 1, 2, 3, or 4), you leave the target digit as it is.
