Question

How do you write 6,000,000 in scientific notation?

Answer 1

Hint:A number is given whose non-zero digit resides at the start of the number. The decimal point is assumed to be after the end of zeros. To express this given number in scientific notation, the first non-zero digit is separated from the second digit (zero or non-zero) by a decimal point. In other words, the decimal point is shifted backwards from the non-zero digits. The zero digits are then indicated in powers of 10.

Complete answer:
Scientific notation is sometimes referred to as the standard index form.The general representation of scientific notation is: \[a{\text{ }} \times {\text{ }}{10^{b\;\;}}\;\] where \[1{\text{ }} \leqslant {\text{ }}a{\text{ }} < {\text{ }}10\] and \[b\] can be any integer. The number \[b\] is known as the order of magnitude while the number \[a\] is referred to as the mantissa or significant. The number \[a\] is the coefficient of the scientific notation and is normally greater than or equal to 1 and less than 10.

The given number is 6,000,000. The non-zero digit is 6. Then according to the condition of significant numbers, these two digits can be separated by a decimal point. Thus we can write it as 6.0 or just 6. Thus, \[a = 6\] and the remaining zeros can be written as power of 10.Thus, \[6,000,000 = 6 \times 1,000,000 = 6.0 \times {10^6}\]. The power factor appears to be \[{10^6}\]. Therefore, \[b = 6\]. This is a positive exponent.

Therefore, 6,000,000 would be written in scientific notation as\[6.0 \times {10^6}\].

Note: The number given in the question has the non-zero digits at the start of the number. In this case, the first non-zero digit is separated from the second digit (zero or non-zero) by a decimal point. Note that the second last digit can be zero or non-zero. But, there are also numbers in which the non-zero digits are at the end of the number. In this case, the last non-zero digit is separated from the second last digit by a decimal point.