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Chapter 4: Problem 57

Simplify. $$ 0.003+3.03 \div 0.01 $$

Short Answer

Expert verified
303.003

Step by step solution

01

Simplify the Division

First, focus on simplifying the division part of the expression. Calculate \(3.03 \div 0.01\). Since dividing by 0.01 is the same as multiplying by 100, calculate: \(3.03 \times 100 = 303\).
02

Add the Results

Now add the result from the division to the remaining part of the expression. So, \(0.003 + 303\).
03

Final Calculation

Perform the addition: \(0.003 + 303 = 303.003\).

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Key Concepts

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

simplifying expressions
Understanding how to simplify expressions is crucial in algebra and daily life. Simplifying helps make problems easier to solve. To simplify, follow specific steps. Look out for different operations such as addition, subtraction, multiplication, and division. When simplifying, follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
In this exercise, first, we simplified the division part before moving to the addition. This approach is efficient and prevents mistakes.
division with decimals
Division with decimals can seem tricky at first, but it's simple once you get the hang of it. When dividing by a decimal, it's often easier to convert the division into multiplication by a whole number. For example, dividing by 0.01 is the same as multiplying by 100. Here's why:
  • 0.01 is 1/100, so dividing by 0.01 is the same as multiplying by the reciprocal of 0.01.
  • Reciprocal of 0.01 is 100.
  • This converts division into multiplication, which is typically simpler.
In the example given, dividing 3.03 by 0.01 converts to multiplying 3.03 by 100, resulting in 303. This simplifies the problem considerably.
addition with decimals
Adding decimals is a fundamental math skill that comes up frequently. Ensure the decimal points are aligned to avoid mistakes.
For the problem in question, after simplifying the division, we added 0.003 to 303.
  • Line up the numbers by their decimal points:
        0.003
    +303.000
  • Perform the addition as you would with whole numbers.
Following this method results in 303.003. Proper alignment makes a huge difference and prevents errors.

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