The Scientific Notation Practice Quiz- I

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 express numbers that are very large or very small, and the exponent represents the number of places the decimal point needs to be moved to create a number between 1 and 10. In the case of a very large number, the decimal point needs to be moved to the left, resulting in a positive exponent.

The given number, 4,500,000, can be expressed in scientific notation as 4.5 x 10^6. In scientific notation, a number is written in the form of a decimal number between 1 and 10, multiplied by a power of 10. In this case, 4.5 is the decimal number and 10^6 represents the power of 10. This indicates that the decimal number should be multiplied by 10 raised to the power of 6, which is equivalent to adding 6 zeros to the end of the decimal number.

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 a negative exponent indicates that the decimal point is shifted to the left. In the case of a very small decimal, the number is less than 1, so the decimal point needs to be shifted to the left, resulting in a negative exponent.

The given expression, 6.5 X 10^4, is in scientific notation. In scientific notation, a number is expressed as a product of a decimal number between 1 and 10 and a power of 10. To convert it to standard notation, we multiply the decimal number (6.5) by 10 raised to the power of the exponent (4). This gives us the answer of 65000. Therefore, the correct standard notation for 6.5 X 10^4 is 65000. The other options provided, 6,5000, 65000., and 6,5000., are incorrect and do not represent the correct conversion.

The given number, 5,345, can be expressed in scientific notation as 5.345x10^3. In scientific notation, the number is written in the form of a decimal number between 1 and 10, multiplied by a power of 10. In this case, 5.345 is the decimal number and 10^3 represents the power of 10, indicating that the decimal point needs to be moved three places to the right to obtain the original number.

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 a power that represents the number of places the decimal point was moved. In this case, the decimal point is moved 5 places to the right, so the exponent is -5.

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 a product of a decimal number between 1 and 10 (inclusive) and a power of 10. The first number, 9.3 x 10^2, is in scientific notation because 9.3 is a decimal number between 1 and 10, and it is multiplied by 10 raised to the power of 2. Similarly, 4 x 10^13 is in scientific notation because 4 is between 1 and 10, and it is multiplied by 10 raised to the power of 13. Lastly, 9.4 x 10^-12 is in scientific notation because 9.4 is between 1 and 10, and it is multiplied by 10 raised to the power of -12.

The given expression is in decimal notation and needs to be converted to scientific notation. In scientific notation, the first step is to move the decimal point to the right until there is only one non-zero digit to the left of the decimal point. In this case, moving the decimal point two places to the right gives 6.0. The second step is to count the number of places the decimal point was moved and use that as the exponent of 10. Since the decimal point was moved two places to the right, the exponent of 10 is -2. Therefore, the expression in scientific notation is 6.0 x 10^-2, which can also be written as 6 x 10^-2.