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Converting Scientific Notation to Decimal Form

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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.

Converting 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.Converting Scientific Notation to Decimal Form
  • 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.Converting Scientific Notation to Decimal Form
Add zeros as needed for placeholders.0.089
 \(8.9×{10}^{-2}=0.089\)
The Check is left to you. 

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