How do you write $297.1$ $297.1$ in scientific notation?

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How do you write $297.1$ $297.1$ in scientific notation?

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Answer 1 · 2016-06-13T05:42:39

$297.1 = 2.971 \times 10^{2}$ $297.1=2.971xx10^2$

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 $10$ $10$ .

Note that moving decimal $p$ $p$ digits to right is equivalent to multiplying by $10^{p}$ $10^p$ and moving decimal $q$ $q$ digits to left is equivalent to dividing by $10^{q}$ $10^q$ .

Hence, we should either divide the number by $10^{p}$ $10^p$ i.e. multiply by $10^{- p}$ $10^(-p)$ (if moving decimal to right) or multiply the number by $10^{q}$ $10^q$ (if moving decimal to left).

In other words, it is written as $a \times 10^{n}$ $axx10^n$ , where $1 \leq a < 10$ $1<=a<10$ and $n$ $n$ is an integer.

To write $297.1$ $297.1$ in scientific notation, we will have to move the decimal point two points to left, which literally means dividing by $10^{2}$ $10^2$ . Hence, we have to multiply by $10^{2}$ $10^2$ too along with shifting decimal point.

Hence in scientific notation $297.1 = 2.971 \times 10^{2}$ $297.1=2.971xx10^2$ .

Answer 2 · 2016-06-14T12:40:08

$2.971 \times 10^{2}$ $2.971xx10^2$

Explanation:

The objective is to have $just one non zero digit to the left of the$ $color(brown)("just one non zero digit to the left of the ")$ $decimal point$ $color(brown)("decimal point")$ . In doing this we change the value so we have to include a $mathematical correction$ $color(magenta)("mathematical correction")$ that, if it were to be applied, would return the new value back to the original number.

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Multiply by 1 but in the form of $1 = \frac{100}{100}$ $1=100/100$

$297.1 \times \frac{100}{100}$ $297.1xx100/100$

Multiplying by 1 in the form of $\frac{100}{100}$ $100/100$ does not change the value but it does change the way it looks.

$\frac{297.1}{100} \times 100$ $297.1/100xx100$

$2.971 \times 100$ $2.971xx100$

$2.971 \times 10^{2}$ $2.971xx10^2$

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How do you write $297.1$ $297.1$ in scientific notation?

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