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In the world of mathematics, there are different systems for representing numbers. Decimal system is one of the most commonly used systems, which is based on the powers of 10. In this system, numbers are represented using digits 0 to 9, and the position of each digit determines its value. In this blog post, we will explore the topic of “What is 5/4 as a decimal” in detail. We will cover the definition of decimals, the conversion of fractions to decimals, and how to simplify fractions to their lowest terms.
What are decimals?
Decimals are a way of representing a number that is not a whole number. The decimal point separates the whole number from its fractional part. For example, the number 2.5 has a whole number part of 2 and a fractional part of 0.5. Decimals are a useful way of representing numbers that are not whole numbers because they allow us to represent numbers to any level of precision.
Converting fractions to decimals
To convert a fraction to a decimal, we divide the numerator (top number) by the denominator (bottom number). For example, to convert the fraction 5/4 to a decimal, we divide 5 by 4:
5 ÷ 4 = 1.25
Therefore, 5/4 as a decimal is 1.25. We can also write this as a mixed number: 1 1/4.
It is important to simplify fractions to their lowest terms before converting them to decimals. To simplify a fraction, we divide both the numerator and the denominator by their greatest common factor (GCF). For example, let’s simplify the fraction 20/100:
The factors of 20 are 1, 2, 4, 5, 10, and 20.
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
The greatest common factor of 20 and 100 is 20.
We divide both the numerator and denominator by 20 to simplify the fraction:
20/100 = 1/5
Now, let’s convert 1/5 to a decimal:
1 ÷ 5 = 0.2
Therefore, 1/5 as a decimal is 0.2.
Converting mixed numbers to decimals
A mixed number is a whole number plus a fraction. To convert a mixed number to a decimal, we first convert the mixed number to an improper fraction, then convert the improper fraction to a decimal. For example, let’s convert the mixed number 3 1/2 to a decimal:
Step 1: Convert the mixed number to an improper fraction:
3 1/2 = (3 × 2 + 1) / 2 = 7/2
Step 2: Convert the improper fraction to a decimal:
7 ÷ 2 = 3.5
Therefore, 3 1/2 as a decimal is 3.5.
Multiplying and dividing decimals
Multiplying and dividing decimals is similar to multiplying and dividing whole numbers. To multiply decimals, we ignore the decimal points and multiply the numbers as if they were whole numbers. The product will have as many decimal places as the sum of the decimal places in the factors. For example, let’s multiply 1.25 by 2:
1.25 × 2 = 2.50
Therefore, the product of 1.25 and 2 is 2.50.
To divide decimals, we move the decimal point in the divisor (bottom number) to the right until it becomes a whole number, then move the decimal point in the dividend (top number) the same number of places to the right. Then we divide the two numbers as if they were whole numbers. For example, let’s divide 2.5 by 0.5:
Step 1: Move the decimal point in the divisor to the right until it becomes a whole number:
0.5 × 10 = 5
Step 2: Move the decimal point in the dividend the same number of places to the right:
2.5 × 10 = 25
Step 3: Divide the two numbers as if they were whole numbers:
25 ÷ 5 = 5
Therefore, the quotient of 2.5 divided by 0.5 is 5.
Adding and subtracting decimals
Adding and subtracting decimals is similar to adding and subtracting whole numbers. We line up the decimal points and add or subtract the numbers as if they were whole numbers. Then we place the decimal point in the answer directly below the decimal point in the numbers being added or subtracted. For example, let’s add 1.25 and 0.75:
Therefore, the sum of 1.25 and 0.75 is 2.00.
In this blog post, we explored the topic of “What is 5/4 as a decimal”. We covered the definition of decimals, the conversion of fractions to decimals, and how to simplify fractions to their lowest terms. We also discussed how to convert mixed numbers to decimals, and how to perform basic operations such as multiplication, division, addition, and subtraction with decimals. Decimals are a fundamental concept in mathematics, and understanding how to work with them is essential in many areas of life, including finance, engineering, and science.