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Write in scientific notation:
| 0.0052 | |
| Move the decimal point to get 5.2, a number between 1 and 10. |
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| Count the number of decimal places the point was moved. | 3 places |
| Write as a product with a power of 10. |
Check your answer:
How can we convert from scientific notation to decimal form? Let’s look at two numbers written in scientific notation and see.
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.
Convert to decimal form:
| Step 1 : Determine the exponent, , on the factor 10. | |
| Step 2 : Move the decimal point places, adding zeros if needed. |
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6,200 |
| Step 3 : Check to see if your answer makes sense. | |
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is 1000 and 1000 times 6.2 will be 6,200.
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Convert to decimal form:
| Determine the exponent , on the factor 10. | The exponent is −2. |
| Move the decimal point 2 places to the left. |
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| Add zeros as needed for placeholders. | 0.089 |
| The Check is left to you. |
We use the Properties of Exponents to multiply and divide numbers in scientific notation.
Multiply. Write answers in decimal form:
| Use the Commutative Property to rearrange the factors. | |
| Multiply 4 by 2 and use the Product Property to multiply by . | |
| Change to decimal form by moving the decimal two places left. |
Divide. Write answers in decimal form:
| Separate the factors. | |
| Divide 9 by 3 and use the Quotient Property to divide by . | |
| Change to decimal form by moving the decimal five places right. |
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