How do you write 297.1 in scientific notation?

Jun 13, 2016

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

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 $10$.

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

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

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

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

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

Jun 14, 2016

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

Explanation:

The objective is to have $\textcolor{b r o w n}{\text{just one non zero digit to the left of the }}$$\textcolor{b r o w n}{\text{decimal point}}$. In doing this we change the value so we have to include a $\textcolor{m a \ge n t a}{\text{mathematical correction}}$ 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 $1 = \frac{100}{100}$

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

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

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

$2.971 \times 100$

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