Question
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Answer
\(8.126 \times 10^6\)
Solution
Step 1. Write the number in scientific notation.
We have
\[
8125568 = 8.125568 \times 10^6.
\]
Step 2. Identify the first four significant figures.
In \(8.125568\), the first four digits are \(8\), \(1\), \(2\), and \(5\).
Step 3. Look at the fifth digit for rounding.
The fifth digit is \(5\) (followed by \(568\)). Since it is \(5\) with nonzero digits after, we round up.
Step 4. Round the number to four significant figures.
Rounding \(8.125568\) to four significant figures gives
\[
8.126 \times 10^6.
\]
Thus, \(8125568\) rounded to four significant figures is
\[
\boxed{8.126\times10^6}.
\]
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Simplify this solution Bonus Knowledge
To express the number 8125568 to four significant figures, we focus on the first four digits, which are 8125. The fifth digit is 5, prompting us to round up. So we write it as 8126 followed by the appropriate number of zeros to retain its place value, resulting in 8,126,000. When dealing with significant figures, remember to consider any leading zeros irrelevant. For example, numbers like 0.0045 also need to be carefully treated, where only the 4 and 5 count as significant!
