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Chapter 5: Problem 150

Explain how to convert from decimal to scientific notation and give an example.

Short Answer

Expert verified
The number \(12345.67\) converts to \(1.234567 脳 10^4\) in scientific notation.

Step by step solution

01

Identifying the Decimal Number

Start with your decimal number that you wish to convert into scientific notation. For this example, let's take the number \(12345.67\).
02

Create a Number Between 1 and 10

Shift your decimal point to the left or right until you have a number between 1 and 10. For the above number, the decimal would be moved four places to the left to get \(1.234567\). The number of places the decimal point is shifted will be the exponent in the scientific notation.
03

Determine the exponent

The number of places moved is the exponent of the 10 in the scientific notation. In this case, since we moved the decimal place four times to the left, the exponent is positive 4. If we had moved the decimal point to the right, the exponent would be negative.
04

Write in Scientific Notation

The final step is to write the number from step 2 multiplied by ten to the power of the exponent from step 3. Thus, the number \(12345.67\) in scientific notation would be \(1.234567 脳 10^4\).

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