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This guide introduces scientific notation, a method for expressing numbers as a coefficient multiplied by a power of ten. Learn how to simplify large and small numbers by rewriting them in scientific notation, using the format: coefficient × 10^exponent. We will explore how to perform calculations, interpret positive and negative exponents, and rewrite typical numbers in scientific form. Whether you're calculating massive figures or small decimals, understand how to use scientific notation efficiently in mathematics.
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Scientific Notation The basics and some math.
Take out your calculator. • Write these calculations and the answer in your notes: • 12,922,341 / 0.011 435 7 = • 1,130,000,000 • 0.05 / 20,111 = • 0.000 002 486 Re-writing numbers in SCIENTIFIC NOTATION makes it so we don’t have to deal with all of these “extra” zeros.
What is it? Scientific Notation(Exponential Notation) • Scientific Notation is used to express any number as: • a number between 1 and 10 • (called a coefficient) • multiplied by 10 • (the “base” as in “base 10”) • raised to a power • (indicated by an exponent) coefficient = 9.13 • 9.13x108 • 9.13E8 exponent = 8
First, let’s review exponents Count the “0”s • 10 = 10 (x 1) = 101 1 • 100 = 10 x 10 = 102 2 • 1,000 = 10 x 10 x 10 = 103 3 • 10,000= 10 x 10 x 10 x 10 = 104 4 • The number in the exponent tells you how many times ten is multiplied by itself.
Reviewing Exponents • Any number raised to the 0 power – or has a 0 in the exponent = 1. • So, 100 = 1
What does this really mean? Scientific NotationBase 10 cont. • 109 would equal a 1 followed by how many zeros? • 9 1,000,000,000 • What would 1.13 x 109 be if written in “long form?” • Move the decimal place to the right 9 places. • 1,130,000,000
When you have a positive exponent, move your decimal to the right the same number of places that are in the exponent.
Let’s rewrite the first number we calculated in scientific notation. • 12,922,341 / 0.011 435 7 = • 1,130,000,000 • 1.13 x 109
What does this really mean? Scientific NotationBase 10 – negative exponents • If the exponent is negative, think division. • 10-1 = 1/(10) = 0.1 • 10-2 = 1/(10 x 10) =1/(100) = 0.01 • 10-3 = 1/(10 x 10 x 10) = 1/(1,000) = 0.001 • 10-4 = 1/(10 x 10 x 10 x 10)= 1/(10,000) = 0.0001
Move the decimal point to the left if you have a negative exponent.
Let’s rewrite our second number in scientific notation. • 0.05 / 20,111 = 0.000 002 486 • Coefficient = 2.486 • The decimal would have to be moved to the left 6 places, so our exponent will be -6. • 2.486 x 10-6
