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?
show the work
1. 0.0000006709 in scientific notation is 6.709 x 10^-7.
2. 9,085,000,000,000 in scientific notation is 9.085 x 10^12.
3. 2.09 x 10^5 in decimal notation is 209,000.
4. 1.98E8 in scientific notation on paper is 198,000,000.
5. To find the size of each lot in scientific notation, we divide the area (3.2 square miles) by the number of lots (1.6 x 10^3).
The calculation is:
3.2 / (1.6 x 10^3) = 2 x 10^-3
So, each lot will be 2 x 10^-3 square miles in size.
1. To write 0.0000006709 in scientific notation, we need to move the decimal point so that there is only one non-zero digit to its left. In this case, we need to move the decimal point 7 places to the right. Therefore, 0.0000006709 can be written as 6.709 x 10^-7 in scientific notation.
2. To write 9,085,000,000,000 in scientific notation, we need to move the decimal point so that there is only one non-zero digit to its left. In this case, we need to move the decimal point 13 places to the right. Therefore, 9,085,000,000,000 can be written as 9.085 x 10^12 in scientific notation.
3. To write 2.09 x 10^5 in decimal notation, we need to multiply the base number (2.09) by 10 raised to the power of the exponent (5). 2.09 x 10^5 equals 209,000.
4. 1.98E8 on a calculator is already in scientific notation. On paper, it would be written as 198,000,000.
5. To determine the size of each lot, we need to divide the area (3.2 square miles) by the number of lots (1.6 x 10^3). In scientific notation, this division would be written as (3.2 x 10^0) / (1.6 x 10^3). Simplifying the division, we get 2 x 10^-3. Therefore, each lot will be 2 x 10^-3 square miles in size.
Sure! Here's how you can solve each of these problems:
1. To write 0.0000006709 in scientific notation, start by moving the decimal point to the right until you have a number greater than or equal to 1. In this case, you need to move the decimal point 6 places to the right. Remember that moving the decimal to the right increases the exponent by the same amount. So, the scientific notation of 0.0000006709 is 6.709 x 10^(-7).
2. To write 9,085,000,000,000 in scientific notation, start by moving the decimal point to the left until you have a number between 1 and 10. In this case, you need to move the decimal point 12 places to the left. Again, remember that moving the decimal to the left increases the exponent by the same amount. So, the scientific notation of 9,085,000,000,000 is 9.085 x 10^(12).
3. To write 2.09 x 10^5 in decimal notation, simply move the decimal point to the right 5 places. The result is 209,000.
4. The expression 1.98E8 on a calculator represents the number 1.98 multiplied by 10 to the power of 8. To write it in scientific notation on paper, we can represent it as 1.98 x 10^8.
5. To find out how big each lot will be in scientific notation, we divide the area, 3.2 square miles, by the number of lots, 1.6 x 10^3. In scientific notation, we can treat it as a regular division problem. Dividing 3.2 by 1.6 gives us 2, and dividing 10^0 by 10^3 (subtracting the exponents) gives us 10^(-3). Therefore, each lot will be 2 x 10^(-3) square miles in scientific notation.