Question

How do you write \[8,720,000\] in scientific notation?

Answer 1

Hint: Use the place value of the leftmost digit to determine the exponential power of \[10\] that needs to be multiplied with the decimal number. To generate the decimal number out of the original number, simply place the decimal after the leftmost digit, so that the leftmost digit of the number becomes the ones digit.

Complete step by step solution:
To express this number in scientific notation, the first thing we need to do is to find out the place value of the leftmost digit in the number. For the given number, the leftmost digit is 8.
The place value of 8 in \[8,720,000\] will be \[8,000,000\] . This is equal to \[8 \times 1,000,000\] .
For scientific notation, we would place the decimal just after the leftmost digit of the number, i.e., just after \[8\] .
The place value of \[8(1,000,000)\] will determine the power of the \[10\] multiplied with the number.
By counting the number of zeroes in the place value of the leftmost digit, we get that the power of \[10\] that will be multiplied with the decimal number is \[6\] .
Now, the decimal number obtained will be \[8.72\] , since the rest of the digits are zeroes, which are considered in the exponential power of \[10\] .
Thus, the term that is to be multiplied with the decimal will be \[{10^6}\] .
Hence, the final representation of \[8,720,000\] in scientific notation will be \[8.72 \times {10^6}\]
So, the correct answer is “ \[8.72 \times {10^6}\] ”.

Note: Scientific Notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be written in decimal form conveniently. A scientific notation consists of a decimal number, which is multiplied with some power of \[10\] .