# Scientific Notation

Learn how to solve mathematics problems containing scientific notation in few simple and easy steps.

## Step by step guide to solve scientific notation problems

• Scientific notation is used to write very big or very small numbers in decimal form.
• In scientific notation all numbers are written in the form of: $$m×10^n$$
 Decimal notation Scientific notation $$5$$ $$5 \times 10^0$$ $$-25,000$$ $$-2.5 \times 10^4$$ $$0.5$$ $$5 \times 10^{ \ -1}$$ $$2,122$$ $$2.122 \times 10^{\ 3}$$

### Example 2:

Write $$0.00015$$ in scientific notation.

Solution:

First, move the decimal point to the right so that you have a number that is between $$1$$ and $$10$$. Then: $$N=1.5$$
Second, determine how many places the decimal moved in step $$1$$ by the power of $$10$$.
Then: $$10^{ \ -4} →$$ When the decimal moved to the right, the exponent is negative.
Then: $$0.00015=1.5×10^{ \ -4}$$

### Example 2:

Write $$9.5 \times 10^{\ -5}$$ in standard notation.

Solution:

$$10^{-5} →$$ When the decimal moved to the right, the exponent is negative.
Then: $$9.5×10^{-5}=0.000095$$

### Example 3:

Write $$0.00012$$ in scientific notation.

Solution:

First, move the decimal point to the right so that you have a number that is between $$1$$ and $$10$$. Then: $$N=1.2$$
Second, determine how many places the decimal moved in step $$1$$ by the power of $$10$$.
Then: $$10^{-4}→$$ When the decimal moved to the right, the exponent is negative.
Then: $$0.00012=1.2×10^{-4}$$

### Example 4:

Write $$8.3×10^{-5}$$ in standard notation.

Solution:

$$10^{-5} →$$ When the decimal moved to the right, the exponent is negative.
Then: $$8.3×10^{-5}=0.000083$$

## Exercises

### Write each number in scientific notation.

1. $$\color{blue}{91 × 10^3}$$
2. $$\color{blue}{60}$$
3. $$\color{blue}{2000000}$$
4. $$\color{blue}{0.0000006}$$
5. $$\color{blue}{354000}$$
6. $$\color{blue}{0.000325}$$

1. $$\color{blue}{9.1 × 10^4}$$
2. $$\color{blue}{6 × 10^1}$$
3. $$\color{blue}{2 × 10^6}$$
4. $$\color{blue}{6 × 10^{–7}}$$
5. $$\color{blue}{3.54 × 10^5}$$
6. $$\color{blue}{3.25 × 10^{–4}}$$

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