1. Write 0.0000006709 in scientific notation
2. Write 9,085,000,000,000 in scientific notation
3. Write 2.09 x 105 in decimal notation.
4. What does 1.98E8 on a calculator look like on your paper in scientific notation?
5. An area that is 3.2 square miles will be divided into 1.6 x 10^3 lots. How big will each lot be in scientific notation?
1. 6.709 x 10^-7
2. 9.085 x 10^12
3. 209,000
4. 198,000,000
5. 2 x 10^0 square miles
1. To write 0.0000006709 in scientific notation, we need to move the decimal point to the right until the number becomes greater than or equal to 1.
0.0000006709 can be rewritten as 6.709 x 10^(-7).
2. To write 9,085,000,000,000 in scientific notation, we need to move the decimal point to the left until there is only one digit to the left of the decimal point.
9,085,000,000,000 can be rewritten as 9.085 x 10^12.
3. To write 2.09 x 10^5 in decimal notation, we need to move the decimal point to the right by 5 places.
2.09 x 10^5 can be rewritten as 209,000.
4. 1.98E8 on a calculator is already in scientific notation. On paper, it would look like 1.98 x 10^8.
5. If an area that is 3.2 square miles is divided into 1.6 x 10^3 lots, we can calculate the size of each lot by dividing the total area by the number of lots.
3.2 square miles / (1.6 x 10^3) lots can be simplified to 0.002 square miles per lot.
Therefore, each lot will be 0.002 square miles in scientific notation.
1. To write 0.0000006709 in scientific notation, you need to move the decimal point to the right until there is only one non-zero digit to the left of the decimal point. Count the number of places you moved the decimal point to determine the exponent.
Starting with 0.0000006709, the decimal point needs to be moved 9 places to the right to get the number 6.709. Thus, the scientific notation is 6.709 x 10^(-9).
2. To write 9,085,000,000,000 in scientific notation, you need to move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. Count the number of places you moved the decimal point to determine the exponent.
Starting with 9,085,000,000,000, the decimal point needs to be moved 12 places to the left to get the number 9.085. Thus, the scientific notation is 9.085 x 10^12.
3. To write 2.09 x 10^5 in decimal notation, you need to move the decimal point to the right or left based on the exponent. In this case, the exponent is positive, so you need to move the decimal point 5 places to the right.
Starting with 2.09, moving the decimal point 5 places to the right gives you the number 209,000. Thus, the decimal notation for 2.09 x 10^5 is 209,000.
4. 1.98E8 on a calculator represents the number 198,000,000. To write it in scientific notation, you need to move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. Count the number of places you moved the decimal point to determine the exponent.
Starting with 198,000,000, the decimal point needs to be moved 7 places to the left to get the number 1.98. Thus, the scientific notation is 1.98 x 10^8.
5. If an area of 3.2 square miles is divided into 1.6 x 10^3 lots, you can find the size of each lot by performing the division.
3.2 square miles / (1.6 x 10^3 lots) = 2 square miles / 10^3 lots.
To express this answer in scientific notation, you need 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, you need to move the decimal point 3 places to the right, so the answer in scientific notation is 2 x 10^(-3) square miles per lot.