Question

How do you write `3.77 times 10^4` in standard notation?

Answer 1

`3.77xx10^3=37700`

Explanation:

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of `10`.

In other words, in scientific notation, a number is written as `axx10^n`, where `1<=a<10` and `n` is an integer and `1<=a<10`.

To write the number in normal or standard notation one just needs to multiply by the power `10^n` (or divide if `n` is negative). This means moving decimal `n` digits to right if multiplying by `10^n` and moving decimal `n` digits to left if dividing by `10^n` (i.e. multiplying by `10^(-n)`).

In the given case, as we have the number as `3.77xx10^4`, we need to move decimal digit to the right by four points. For this, let us write `3.77` as `3.770000` and moving decimal point four points to right means `37700.00`

Hence in standard notation `3.77xx10^3=37700`

Answer 2

`3.77xx10^4 -=37700`

Where `-=` means equivalent to.

Explanation:

`color(brown)(3.77xx10=37.7)color(blue)(" "larr" "3.77xx10^1=37.7)`

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`color(brown)(3.77xx10xx10=377color(blue)(" "larr 3.77xx10^2=377)`

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`color(brown)(3.77xx10xx10xx10=3770color(blue)(" "larr 3.77xx10^3=3770)`

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`color(brown)(3.77xx10xx10xx10xx10=37700color(blue)(" "larr 3.77xx10^4=37700)`