Write the number 5,730,000,000,000,000 in scientific notation.

Step-by-step solution

1. 1

   Recall the required form. Scientific notation is $a\times 10^{n}$ where $1\le |a|<10$ and $n$ is an integer. So the coefficient must have exactly one non-zero digit before the decimal point.

2. 2

   Place the decimal point after the first digit. The digits are $5{,}73$ followed by zeros, so the coefficient is

   $a=5.73.$

   Trailing zeros are dropped from the coefficient — they are carried by the power of ten instead.

3. 3

   Count how far the point moved. In the original, the (invisible) decimal point sits at the far right, after $16$ digits. Moving it to just after the $5$ takes $15$ places to the left:

   $5\underbrace{730000000000000}_{15\ \text{digits}}.$

4. 4

   Choose the sign of the exponent. The number is large (greater than $10$), so the exponent is positive:

   $n=+15.$

   A leftward move of the point always pairs with a positive exponent, because you are compensating for having made the coefficient smaller.

5. 5

   Write the answer and check it.

   $5{,}730{,}000{,}000{,}000{,}000=5.73\times 10^{15}.$

   Expanding back, $5.73\times 10^{15}$ moves the point $15$ places right, giving $5730000000000000$ — the original number, with $15$ digits after the leading $5$.