Write these numbers in standard notation. 3.05 x 10–3 8.92 x 106

Write these numbers in standard notation. 3.05 x 10–3 8.92 x 106

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  1. the direct variation says that:

    [tex]y \propto x[/tex]

    then the equation is of the form is given by:

    [tex]y = kx[/tex]             where k is the constant variation.

    from the given table:

    consider any value of x and m(x)=y

    x = 2 and m(x)=y = 3

    substitute these value in [1]; we have;

    [tex]3 = 2k[/tex]

    divide both sides by 2 we get;

    [tex]k =\frac{3}{2} = 1.5[/tex]

    ⇒[tex]m(x) = 1.5x[/tex]

    check:

    put x = -1 and m(x) = -1.5

    substitute in the equation:

    [tex]m(x) = 1.5x[/tex]

    [tex]-1.5 = 1.5(-1)[/tex]

    -1.5 = -1.5                   true

    therefore, the function m(x) represents a direct variation

    graph of this function as shown below:

  2. 0.00305 & 8920000

    Step-by-step explanation:

    3.05 × (10^-3)

    3.05 ÷ 10³

    3.05 ÷ 1000 = 0.00305

    8.92 × 10⁶

    8.92 × 1000000 = 8920000

  3. We have been given the two numbers:

    [tex]3.05 \cdot 10^{-3}[/tex]

    And [tex]8.92\cdot 10^{6}[/tex]

    [tex]x^{-a}=\frac{1}{x^a}[/tex]

    [tex]10^{-3}=\frac{1}{10^3}=\frac{1}{1000}[/tex]

    So, [tex]3.05 \cdot 10^{-3}=\frac{3.05}{1000}[/tex]

    [tex]\Rightarrow 0.00305[/tex]

    And [tex]8.92\cdot 10^{6}=\frac{892}{100}\cdot {1000000}[/tex]

    [tex]892\cdot 10000[/tex]

    [tex]\Rightarrow 8920000[/tex]

    [tex]3.05 \cdot 10^{-3}=0.00305[/tex]

    [tex]8.92\cdot 10^{6}=8920000[/tex]

  4. The number 3.05*10⁻³ in standard notacion is 0.00305.

    The number 8.92*10⁶ in standard notation is 8,920,000.

    Explanation:

    Scientific notation is a quick way to represent a number using base ten powers. This notation is used to express very large or very small numbers very easily.

    The numbers are written as a product:

    a * 10ⁿ

    where:

    a is a real number greater than or equal to 1 and less than 10, to which a decimal point is added after the first digit if it is a number that is not an integer. n is an integer, which receives the name of exponent or order of magnitude. Represents the number of times the comma moves. It is always an integer, positive if it moves to the left, negative if it moves to the right.

    In numbers where the exponent of ten is negative, like in this case of 3.05*10⁻³, you must move the comma to the left as many positions as the exponent marks. After moving the comma the first place to the left, there is a zero followed by the comma and behind the figures we had in scientific notation. Then, for each place that is missing, you have to add a zero to the left, being at all times behind the comma. So, in this case, the number 3.05*10⁻³ in standard notacion is 0.00305.

    In numbers where the exponent of ten is positive, you must move the comma to the right as many positions as the exponent that has the ten mark. If you don't have more places to move the comma but we still have positions to move, then you will have to add zeros for each missing position. So, in this case, the number 8.92*10⁶ in standard notation is 8,920,000.

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