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Chapter 1: Problem 627

Convert each fraction to a decimal. $$ 2.4+\frac{5}{8} $$

Short Answer

Expert verified
3.025

Step by step solution

01

Identify Components

Recognize the two components of the expression: the decimal number 2.4 and the fraction \( \frac{5}{8} \).
02

Convert Fraction to Decimal

Convert the fraction \( \frac{5}{8} \) to a decimal by performing the division. \(5 \div 8 = 0.625\).
03

Add the Decimal Numbers

Add the decimal equivalent from Step 2 to the given decimal number. \( 2.4 + 0.625 \).
04

Simplify the Addition

Perform the addition: \( 2.4 + 0.625 = 3.025 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Converting Fractions
Understanding how to convert fractions into decimals is a vital skill in mathematics. A fraction represents a division. So, converting a fraction \(\frac{a}{b}\) into a decimal simply involves dividing the numerator (top number) by the denominator (bottom number).
Here is a step-by-step approach:
  • Write down the fraction \(\frac{a}{b}\).
  • Perform the division \(\frac{a}{b}\).
  • Use a calculator if necessary for precise results.
Let鈥檚 use an example: Convert \(\frac{5}{8}\) to a decimal. Perform the division 5 梅 8 which equals 0.625. Now, \(\frac{5}{8} = 0.625\).This method can be used for any fraction.
Decimal Addition
Adding decimals is another essential skill that complements your ability to work with fractions. It is crucial to carefully align the decimal points to ensure accuracy. Here鈥檚 an easy way to perform decimal addition:
  • Align the numbers vertically by their decimal points.
  • Add the numbers as you would for whole numbers, starting from the rightmost digit.
  • If necessary, insert extra zeros to make sure each number has the same number of decimal places before adding.
Let鈥檚 consider an example: Add 2.4 and 0.625.
  • Align the decimal points:
    $$ \begin{array}{r} 2.400 \ +0.625 \ \ \ \ \ \ \ \ \ \ \ \ 3.025 \ \ \ \ \ \
So, we have 2.4 + 0.625 which equals 3.025.
Arithmetic Operations
Understanding arithmetic operations is fundamental in solving various mathematical problems. The primary operations include addition, subtraction, multiplication, and division. Here we鈥檒l focus on addition and some tips to ease the process:
  • Always start addition from the rightmost digit.
  • Align numbers properly based on their place value (e.g., units, tens, hundreds).
  • Use carrying over, bringing any extra value to the next higher place value when the sum exceeds 9.
In the context of our example, adding 2.4 + 0.625:
  • Line up the decimal points (as seen in section 2).
  • Add each digit, working from right to left:
  • First digit: 0.000 + 0.625 gives 0.625 (place 0 and carry 6)
  • Second Digit: 4.000 + 2.000 + 0.6 (carry over) gives 6. (place 0 and carry 1)
  • Third Digit: 2.000 + 0.1 gives 2.0 (add final carry over 1, resulting in 3.025)
So, the total of 2.4 + 0.625 gives us a sum of 3.025.

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