Mathematics » Introducing Polynomials » 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.

$$\begin{array}{cccc}9.12\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}\hfill & \phantom{\rule{2em}{0ex}}& & 9.12\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\hfill \\ 9.12\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}10,000\hfill & \phantom{\rule{2em}{0ex}}& & 9.12\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}0.0001\hfill \\ 91,200\hfill & \phantom{\rule{2em}{0ex}}& & 0.000912\hfill \end{array}$$

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.

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

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

### Solution

 Step 1: Determine the exponent, $$n$$, on the factor 10. $$6.2×{10}^{3}$$ Step 2: Move the decimal point $$n$$ 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. 6,200 Step 3: Check to see if your answer makes sense. $${10}^{3}$$ is 1000 and 1000 times 6.2 will be 6,200. $$6.2×{10}^{3}=6,200$$

### How 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

 $$8.9×{10}^{-2}$$ Determine the exponent $$n$$, on the factor 10. The exponent is −2. Move the decimal point 2 places to the left. Add zeros as needed for placeholders. 0.089 $$8.9×{10}^{-2}=0.089$$ The Check is left to you.