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Scientific Notation

Scientific notation is the expression of a number based on the largest exponent of 10 for its value, where the form is a decimal number A x 10n.

6,389 Questions

What is the result of (6.2 and times 10 4) x (3.3 and times 10 2) expressed in scientific notation?

When multiplying exponents, you add them. So, 10^4 x 10^2 = 10^6. Now 6.2 x 3.3 = 20.46. So, you would have 20.46 x10^6, but we want the number in front of the x10 to be less than 10 and greater than 1, so the answer would be 2,046x10^7 (move the decimal one to the left, and increase the exponent by 1).

What are the steps to subtract in scientific notation?

  1. Convert the numbers so that they all have the same index for 10.
  2. Calculate the subtraction for the mantissae, ignoring the powers of 10.
  3. Add back the power of 10 term.
  4. Adjust the power, if necessary, so that the mantissa of the answer is in the range [1, 10).

Example:

1.23*10^3 - 3.4*10^2

Convert them so that the power of 10 is 2:

12.3*10^2 - 3.4*10^2 = (12.3 - 3.4)*10^2 = 8.9*10^2.

{there is no need to adjust the power of 10).

Or

Convert them so that the power of 10 is 3: 1.23*10^2 - 0.34*10^3 = (1.23 - 0.34)*10^3 = 0.89*10^3 and now you need to adjust because the mantissa is less than 1. So 8.9*10^2.

What is 1.23x10-5 in scientific notation?

1.23x10-5 in scientific notation is 1.23 x 10-5

This equates to 0.0000123 in standard notation.

What is 1 billion in scientific notation?

Scientific notation is is a great way to shorten long numbers. When you use scientific notation, you are counting the number of place the decimal has to move in order to get the short form of the number. For 1 billion, it would be 1 x 10^9 because the decimal point had to shift 9 times.