Scientific notation

Scientific notation

Scientific notation is a way of writing number. It is especially useful when we want to express very large and small numbers. There are two parts in scientific notation. The first part consists of digits, and the second part is x 10 to a power.
Basic concepts: Using exponents to describe numbers, Exponent rules, Order of operations with exponents,
Related concepts: Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)}, Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)}, Exponents: Negative exponents,

Lessons

  • Introduction
    What is scientific notation?
    • How to convert scientific notations to numbers?
    • How to convert numbers to scientific notations?
  • 1.
    Write the number in scientific notation
    a)
    23660000

    b)
    0.00034320000

    c)
    133.4×105 \times {10^{5}}

    d)
    0.000346×10−9 \times {10^{-9}}

  • 2.
    Write the number in standard notation
    a)
    1.863×1013 \times {10^{13}}

    b)
    -3.64 ×10−9 \times {10^{-9}}

  • 3.
    Calculate the following scientific notations
    a)
    (0.005×10−3)(2.9×10−6)= (0.005 \times {10^{-3}} )(2.9 \times {10^{-6}} ) =

    b)
    (6.75×103)/(0.02×10−3)=(6.75 \times {10^3} )/(0.02 \times {10^{-3}} ) =

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19.
Indices
19.1
Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)}
19.2
Indices: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
19.3
Indices: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)}
19.4
Indices: Negative exponents
19.5
Indices: Zero exponent: a0=1 a^0 = 1
19.6
Indices: Rational exponents
19.7
Combining laws of indices
19.8
Scientific notation
19.9
Convert between radicals and rational exponents
19.10
Solving for indices
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