Scientific Notation Questions & Answers Quiz

Scientific Notation is a system for writing very large or very small numbers more easily and quickly. It allows us to express these numbers in a concise and standardized format by using powers of 10. This format is particularly useful in scientific fields where extremely large or small numbers are commonly encountered, such as in astronomy or microbiology. By using scientific notation, we can easily compare and perform calculations with these numbers without having to write out all the zeros.

When converting a very large number into scientific notation, the exponent of the 10 will always be positive. This is because scientific notation is used to represent numbers that are very large or very small, and the exponent of the 10 indicates the number of places the decimal point must be moved to obtain the original number. In the case of a very large number, the decimal point needs to be moved to the left, resulting in a positive exponent.

When converting a very small decimal into scientific notation, the exponent of the 10 will always be negative. This is because scientific notation is used to represent numbers that are very large or very small, and when the number is very small, the decimal point needs to be moved to the left. This means that the exponent of the 10 will be negative, indicating that the decimal point has been moved to the left by a certain number of places.

In a number where you can't see the decimal, like 43,789, the decimal is always 'hiding' to the right or right side of the last number.

The given number, 5,345, can be written in scientific notation as 5.345x10^3. In scientific notation, the number is expressed as a decimal between 1 and 10, multiplied by a power of 10. In this case, the decimal is 5.345 and the power of 10 is 3, indicating that the decimal needs to be multiplied by 10 raised to the power of 3.

The given number, 0.000000312, can be expressed in scientific notation as 3.12x10^-7. In scientific notation, the number is written as a decimal between 1 and 10, multiplied by a power of 10. In this case, the decimal is 3.12, and it is multiplied by 10 raised to the power of -7, indicating that the decimal point is shifted 7 places to the left.

In scientific notation, the number in front of the decimal represents the coefficient or mantissa. It is always a positive integer or one. This is because scientific notation is used to express very large or very small numbers, and the coefficient must be a number between 1 and 10. If the coefficient is less than 1, it is expressed as a decimal greater than 0 and less than 1, such as 0.5. Therefore, "one" and "1" are both correct answers as they represent the required number in scientific notation.

The given number, 0.000076, can be written in scientific notation as 7.6x10^-5. In scientific notation, the decimal point is moved to the right of the first non-zero digit, and the resulting number is multiplied by 10 raised to the power of the number of places the decimal point was moved. In this case, the decimal point is moved five places to the right, resulting in a coefficient of 7.6, and the number is multiplied by 10 raised to the power of -5.

The given question asks to write the number 10,055 with its decimal shown. The answer provided is 10,055., which includes a decimal point after the last digit. This indicates that the number is a whole number and does not have any fractional or decimal part.

The numbers that are correctly written in scientific notation are 9.3 x 10^2, 4 x 10^13, and 9.4 x 10^-12. In scientific notation, a number is written as the product of a decimal number between 1 and 10 and a power of 10. The first number, 9.3 x 10^2, represents 9.3 multiplied by 10 raised to the power of 2, which is 930. The second number, 4 x 10^13, represents 4 multiplied by 10 raised to the power of 13, which is a very large number. The third number, 9.4 x 10^-12, represents 9.4 multiplied by 10 raised to the power of -12, which is a very small number.

The given number, 1,098,444, can be written in scientific notation as 1.098x10^6. In scientific notation, the number is represented as a decimal number between 1 and 10 (in this case, 1.098) multiplied by a power of 10 (in this case, 10^6).