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Chapter 5: Problem 63

Express each number in scientific notation. 32,000

Short Answer

Expert verified
The scientific notation of 32000 is \(3.2 \times 10^4\).

Step by step solution

01

Identify the significant figures and decimal location

Identify the significant numbers in 32,000 which are 32. The rest are just zeroes. If there's a decimal point, it's currently implicitly at the end of the number, i.e., 32,000.
02

Place the decimal after the first significant figure

Place a decimal point after the first significant figure. Here, it is after 3, which gives us '3.2'. This is the number part of the scientific notation.
03

Count the number of places the decimal has moved

Count how many places the decimal point moved from the original location to the new one - this is the exponent on 10. From the end of 32000 to just after 3, it has moved 4 places to the left.
04

Write the scientific notation

The scientific notation of 32000 is then written as follows: multiply the number from Step 2 by 10 raised to the power equal to the number of spaces moved which is 4. Therefore, the scientific notation of 32000 is \(3.2 \times 10^4\).

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