Mathematics » Polynomials II » Integer Exponents and Scientific Notation

# Converting Scientific Notation to Decimal Form

## Converting Scientific Notation to Decimal Form

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:

1. Determine the exponent, $$n$$, on the factor 10.
2. 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.
3. 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.

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