Real number calculator

Work with decimals

The calculator makes basic and advanced operations with real numbers, natural numbers, integers, rational and irrational numbers. It also shows detailed step-by-step information about calculation procedure. Solve problems with two, three, or more real numbers in one expression. Add, subtract, and multiply real numbers step-by-step. This calculator performs addition, subtraction, multiplication, or division for calculations on positive or negative real numbers. This online real number calculator will help you understand how to add, subtract, multiply, or divide real numbers.

Real numbers are numbers that can be found on the number line. This includes the natural numbers( 1,2,3 ...), integers (-3) rational (fractions) and irrational numbers (like √2 or π). Positive or negative, large or small, whole numbers or decimal numbers are all real numbers. Imaginary numbers and complex numbers cannot be draw in number line, but in complex plane.

Examples:

• addition of real numbers: -3/2 + pi/2
• subtraction of real numbers: 32.14 - 67.32
• parenthesis: sin(pi/2) * (1.1+2.2+3.3)
• Complex example: Priority of operators and brackets: 3⋅[8−(−1) + (−3)÷(−3)]^2

Real numbers in word problems:

  • Evaluate 18
    Evaluate the expression (-4-7i)-(-6-9i) and write the result in the form a+bi (Real + i* Imaginary).
  • Fruit punch 2
    Alberto makes fruit punch with 24.2 ounces of apple juice and 18.4 ounces of pineapple juice. He splits the fruit punch equally into 6 glasses. How much fruit punch is in each glass?
  • Is equal
    Is equal following terms? -9 21 = (-9) 21
  • The diameter 2
    The diameter of the Earth is 12,756 kilometers. If Mercury's diameter is about 7,876.6 kilometers shorter than that of the Earth, what is the diameter of Mercury?
  • Write 3
    Write a real-world problem involving the multiplication of a fraction and a whole number with a product that is between 8 and 10, then solve the problem.
  • Imaginary numbers
    Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is its sum?
  • Is complex
    Are these numbers 2i, 4i, 2i + 1, 8i, 2i + 3, 4 + 7i, 8i, 8i + 4, 5i, 6i, 3i complex?
  • Complex plane mapping
    Show that the mapping w = z +c/z, where z = x+iy, w = u+iv and c is a real number, maps the circle |z| = 1 in the z-plane into an ellipse in the (u, v) plane.
  • Equation with abs value
    How many solutions has the equation (|x| +x) |x-3| = |x+1| in the real numbers?
  • Subtract 4
    Subtract the following decimals. a. 0.98 - 0.053 b. 0.67 - 0.4 c. 0.3 - 0.002 d. 3.2 - .789 e. 6.53 - 4.298 f. 6 - 4.32 g. 7 - 3.574 h. 4.83 - 1.8 i. 3.7 - 1.8 j. 16.17 - 11.632
  • On the number line
    What number is exactly in the middle between 9.8 and -2.4 on the number line?
  • Which 8
    Which among the following real numbers below is the least? A. 5/8 B. 0.75 C. 7/10 D. 35/99
  • The sum 15
    The sum of the real numbers x and y is 24. Their difference is 12. What is the value of xy?
  • Two midpoints
    Point A is on a number line halfway between -17 and 5 . Point B is halfway between Point A and 0. What integer does Point B represent?
  • Exponential equation
    Solve exponential equation (in real numbers): 98x-2=9
  • Logarithmic equation
    Solve equation: log13(7x + 12) = 0
  • Open intervals
    Open intervals A = (x-2; 2x-1) and B = (3x-4; 4) are given. Find the largest real number for which A ⊂ B applies.

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