Let’s dive into decimals and fractions, two concepts you’re definitely going to encounter in exams like the SAT, ACT, and even the GRE or AP tests! A decimal number is simply a combination of a whole number and its fractional part, and they’re separated by a decimal point. You’ve seen this before when you write numbers like 2.75—2 is the whole number, and .75 is the fractional part. Easy, right?

Now, decimals and fractions are closely related, and you can convert one to the other with just a few simple steps. For example, if you have a decimal like 2.75, you can easily convert it to a fraction by ignoring the decimal point and treating it as 275/100. After that, you can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). So 275/100 simplifies to 11/4. You’ll definitely see questions about converting between decimals and fractions in your exams, and knowing how to do this quickly will give you a major advantage!

We also use decimals and fractions in our everyday life, especially when we’re dealing with money, measurements, and even in scientific fields. Understanding the relationship between these two forms of numbers is super helpful. For example, if you’re shopping and the price is listed as $3.75, you can think of it as 375/100 or $3 and 75 cents.

In this article, we’ll explore the types of decimals and fractions, how place values work, and how these concepts tie into percentages. We’ll also look at some real-world applications, and give you solved examples to help you get a better grasp on how to convert decimals to fractions and work with them in different situations. Whether you're gearing up for the SAT, ACT, or even the MCAT, understanding these basics will definitely help you feel more confident when those questions pop up!

What are Decimals?

Decimals are sets of numbers that are written with a decimal point in them. A decimal number has two parts, the one on the left of the decimal point are whole numbers of integers, and the one to the right of the decimal point are decimal numbers. In order to compare decimals or solve problems related to decimals, the place value of the decimal numbers should be carefully observed and noted.

As we know that the decimal number has two parts, the place value for the whole number part of the decimal number is the same as any other number. But, for the decimal part of the number, the representation is a bit different and we make use of decimal values to represent them. We need to understand that as we move left, every next number is ten times greater than the previous number.

 So, we can say it as to the right of the one’s place, we have tenths place (1/10), to the right of tenths place we have hundredths place (1/100), and so on.

Reading Decimal Numbers

Reading of decimal numbers can be done in two different ways. The first is to read the whole number followed by the decimal and then read the digits of the decimal part one by one separately.

For example: Any decimal number 78.56 can be read as seventy-eight point five-six. Let us take another example:

In the second method, the whole number portion is read first, followed by the word "and," and then the fractional portion is read in the same way as whole numbers, but is then followed by the place value of the last digit.

For example: Any decimal number 78.56 can be read as seventy-eight and fifty-six hundredths. Let us take another example:

Numerator and Denominator of Fractions

We know that a fraction is the part of the whole. We can represent the fractions as a/b, where a and b both are integers. The integer above the bar is termed as the numerator and that below the bar is the denominator.

The number with equal parts is stated in the numerator, and the number of parts of the given number is stated in the denominator. Let us check some of the conditions for the fractions:

• When the value of the numerator is equal to that of the denominator, then the fraction is 1.
• The fraction is 0, when the value of the numerator is 0.
• The fraction goes to infinity, when the value of the denominator is 0.
• When the digits after the decimal keeps on repeating, the decimal fraction is known as the recurring decimal.

Place Value of Decimal Fractions

We are aware that the order of the digits for the whole number is ones, tens, hundreds, thousands, ten-thousands, and so on, going from right to left.

In case of decimal numbers, as we are dealing with decimal points, the place value of the digit is taken from left to right in the order: tenths, hundredths, thousandths, and ten-thousandths.

Types of Decimal Fractions

The fractions with denominators in multiples of 10 are the decimal fractions. In mathematics, we have studied several types of decimal like:

• Terminating Decimals: The decimal numbers that have a finite number of digits after the decimal point are termed as terminating decimals.
• Recurring Decimals: The decimal numbers that have repeating digits after the decimal point are termed as recurring decimals.
• Non-Recurring Decimals: The decimal numbers that have non-repeating digits after the decimal point are termed as non-recurring decimals.
• Non-Terminating Decimals: The decimal numbers that have an infinite or non-terminating number of digits after the decimal point are termed as terminating decimals.

Visualizing Decimal Numbers

Decimal numbers can be represented using Base-10 blocks. A flat represents one whole unit, a rod one-tenth of the whole, and a block one-hundredth of the whole. 

Let us understand this using an example:

If we need to represent 25.78, this means we have 25 whole units, which means 2 cubes and 5 flats, 7 rods, and 8 blocks. 

There is another way to represent decimals using an abacus:

Decimals and Fractions

All the decimal numbers can be represented in the form of fractions. This can be done using two simple steps to convert a decimal to fractions. The first step is to ignore the decimal point and then write the number with the power of 10 depending on the decimal places. 

For example: Consider the number 0.25, this can be written as 25/100, which on solving becomes 1/4.

Also, a recurring decimal can be written as a fraction. A decimal number .0333 is written in fractions as 1/3. It is to be noted that most of the decimal numbers can be converted to fractions easily. 

Let us check an example:

In a similar manner, a fraction can be converted to decimals by using two methods. First method involves long-division and the other involves multiplying the numerator and denominator through fractions to get the multiples of 10 like 10, 100, 1000, etc.

Decimals and Percentage

Just like fractions, decimals can also be expressed in the form of percentage. We generally need to convert decimals to percentages when we compare two numbers. 

This conversion of decimals to percentages can be done using a simple method. This involves multiplying a number by 100%. This will move the decimal point two places towards the right. This is followed by a percentage sign. 

For example: 0.78 = 0.78 * 100% = 78%

In the same way we can convert percentage to decimal. This is done by dividing the given percentage by 100 and removing the decimal point. Further the fraction is simplified to get the decimal number.

Decimals in Everyday Life

Decimals play a significant role in daily life for calculating precise amounts of money, weight, temperature, length, and other quantities. Decimals allow us to represent a portion of a unit. Moreover, decimals can be used to indicate very small numerical quantities.

Decimals and Fractions Solved Examples

Que 1: Sam purchased 100 apples from a fruit vendor nearby, but discovered later that five of them were spoiled. Can you calculate the decimal and fractional parts of the rotting apples to the total number of apples Jim purchased?

Ans 1: Given that:

5 apples out of 100 were spoiled. 

So, the fraction of rotten apples to the total number of apples is given as 5/100.

To convert this fraction into decimal we need to divide the numerator 5 with the denominator 100.

This can be done by simply taking two decimal places. 

Therefore, the decimal answer is 0.05. 

Que 2: What is the decimal form of 6/1000?

Ans 2: To find the decimal form of a number we divide its numerator by the denominator.

Here, we can simply take three decimal places.

Therefore, the decimal form of 6/1000 = 0.006.

Conclusion

In conclusion, understanding decimals and fractions is essential not only for exams like the SAT, ACT, or GRE but also for everyday life. Whether you're converting between the two or dealing with percentages, knowing how to handle these concepts can make math much easier. With practice, you'll be able to tackle problems involving decimals and fractions with confidence, ensuring you're ready for whatever challenges come your way in tests or real-world situations!