Add And Subtract Scientific Notations Worksheet

Algebra 1
Scientific Notation

Total questions - 6

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How Will This Worksheet on "Add and Subtract Scientific Notations" Benefit Your Student's Learning?

  • Develops fluency in applying steps for operations with scientific notation through multiple examples.
  • Enhances problem-solving skills with various scientific notation problems.
  • Reinforces understanding of place value and exponents.
  • Shows real-life applications and provides immediate feedback.
  • Offers practice at different levels, preparing students for advanced mathematical concepts.

How to Add and Subtract Scientific Notations?

  • Identify the coefficients (the numbers before the "`x10`") and exponents (the powers of `10`) of the two numbers written in scientific notation.
  • If the exponents are different, adjust the exponents to be the same by moving the decimal point in the coefficient with the smaller exponent to the left or the coefficient with the greater exponent to the right. The number of places to move the decimal point is equal to the difference between the two exponents.
  • Add or subtract the coefficients after adjusting the exponents to be the same.
  • Write the answer in scientific notation by combining the adjusted coefficient and the adjusted exponent.

Solved Example

Q. Subtract. Write your answer in scientific notation.\newline(7.15×105)(5.964×105)(7.15 \times 10^5) - (5.964 \times 10^5)\newlineChoices:\newline(A) 1.186×1071.186 \times 10^7\newline(B) 1.186×1061.186 \times 10^6\newline(C) 1.186×1051.186 \times 10^5\newline(D) 1.186×1041.186 \times 10^4
Solution:
  1. Subtract coefficients, keep exponent: Subtract the coefficients of the given numbers while keeping the exponent the same since they are like terms. 7.155.964=1.1867.15 - 5.964 = 1.186
  2. Write final answer in scientific notation: Write the final answer in scientific notation using the common exponent from the original terms. 1.186×1051.186 \times 10^5
  3. Choose equivalent expression: Choose the equivalent expression for the final answer from the given choices.\newlineThe correct choice is (C)1.186×105(C)1.186 \times 10^5
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About Worksheet

Algebra 1
Scientific Notation

Adding and subtracting numbers in scientific notation involves aligning the exponents, then either adding or subtracting the coefficients accordingly. This method simplifies calculations with large or small numbers by standardizing the exponents and adjusting the coefficients to maintain the correct order of magnitude. It's essential in scientific and engineering contexts for precise computations and data analysis, ensuring accuracy when dealing with measurements spanning wide ranges of values.

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