## Converting Scientific Notation to Decimal Form

Contents

How can we convert from scientific notation to decimal form? Let’s look at two numbers written in scientific notation and see.

\(\begin{array}{cccc}\hfill 9.12\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}\hfill & & & \hfill \phantom{\rule{4em}{0ex}}9.12\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\hfill \\ \hfill 9.12\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}10,000\hfill & & & \hfill \phantom{\rule{4em}{0ex}}9.12\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}0.0001\hfill \\ \hfill 91,200\hfill & & & \hfill \phantom{\rule{4em}{0ex}}0.000912\hfill \end{array}\)

If we look at the location of the decimal point, we can see an easy method to convert a number from scientific notation to decimal form.

\(\begin{array}{cccc}\hfill 9.12\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}=91,200\hfill & & & \hfill \phantom{\rule{4em}{0ex}}9.12\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}=0.000912\hfill \end{array}\)

In both cases the decimal point moved 4 places. When the exponent was positive, the decimal moved to the right. When the exponent was negative, the decimal point moved to the left.

### Example: How to Convert Scientific Notation to Decimal Form

Convert to decimal form: \(6.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}.\)

### Solution

The steps are summarized below.

### Convert scientific notation to decimal form.

To convert scientific notation to decimal form:

- Determine the exponent, \(n\), on the factor 10.
- Move the decimal \(n\) places, adding zeros if needed.
- If the exponent is positive, move the decimal point \(n\) places to the right.
- If the exponent is negative, move the decimal point \(|n|\) places to the left.

- Check.

## Example

Convert to decimal form: \(8.9\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}.\)

### Solution

Determine the exponent, n, on the factor 10. | |

Since the exponent is negative, move the decimal point 2 places to the left. | |

Add zeros as needed for placeholders. |