# Operations and Numbers in Scientific Notation Foundations of Algebra.

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Operations and Numbers in Scientific Notation Foundations of Algebra

Adding/Subtracting when Exponents are Equal When the exponents are the same for all the numbers you are working with, add/subtract the base numbers then simply put the given exponent on the 10.

Example 1 Given: 2.56 X 10 3 + 6.964 X 10 3 Add: 2.56 + 6.964 = 9.524 Answer: 9.524 X 10 3

Example 2 Given: 9.49 X 10 5 – 4.863 X 10 5 Subtract: 9.49 – 4.863 = 4.627 Answer: 4.627 X 10 5

Adding/Subtracting when the Exponents are Different

When adding or subtracting numbers in scientific notation, the exponents must be the same. If they are different, you must move the decimal either right or left so that they will have the same exponent.

Moving the Decimal For each move of the decimal to the right you have to add -1 to the exponent. For each move of the decimal to the left you have to add +1 to the exponent.

Continued… It does not matter which number you decide to move the decimal on, but remember that in the end both numbers have to have the same exponent on the 10.

Example 1 Given: 2.46 X 10 6 + 3.476 X 10 3 Shift decimal 3 places to the right for 10 6. Move: 2460 X 10 6-3 Add: 2460 X 10 3 + 3.476 X 10 3 Answer: 2463.476 X 10 3 Answer: 2.463476 X 10 6

Example 2 Given: 5.762 X 10 3 – 2.65 X 10 -1 Shift decimal 4 places to the left for 10 -1. Move:.000265 X 10 (-1+4) Subtract: 5.762 X 10 3 -.000265 X 10 3 Answer: 5.762 X 10 3

Multiplying and Dividing Reminders: 1)The first number must be between 1 and 10 2)Make sure your decimal point is VERY clear 3)Number larger than one has a positive exponent 4)Number smaller than one has a negative exponent

Multiplying with Scientific Notation Add the Exponents 10 2 X 10 3 = 10 5 100 X 1000 = 100,000

Multiplying with Scientific Notation (2.3 X 10 2 )(3.3 X 10 3 ) 230 X 3300 Multiply the Coefficients 2.3 X 3.3 = 7.59 10 2 X 10 3 = 10 5 Add the Exponents 7.59 X 10 5 759,000

Multiplying with Scientific Notation (4.6 X 10 4 ) X (5.5 X 10 3 ) = ? (3.1 X 10 3 ) X (4.2 X 10 5 ) = ?

Dividing with Scientific Notation Subtract the Exponents 10 4 /10 3 = 10 1 10000/ 1000 = 10

Dividing with Scientific Notation (3.3 X 10 4 )/ (2.3 X 10 2 ) 33000 / 230 = 143.4783 Divide the Coefficients 3.3/ 2.3 = 1.434783 10 4 / 10 2 = 10 2 Subtract the Exponents 1.4347823 X 10 2 143.4783

Dividing with Scientific Notation (4.6 X 10 4 ) / (5.5 X 10 3 ) = ? (3.1 X 10 3 ) / (4.2 X 10 5 ) = ?

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