Sam is comparing the half-life of two isotopes of uranium. The half-life of Uranium-238 is 4.5 × 10° years. The half-life of Uranium-233 is 1.6 x 105 years. He computed how much greater the half-life of Uranium-238 is than that of Uranium-233, and his calculator displayed the number 2.814. What is this number in scientific notation? (1 point)
2.81 × 10
2.81 + 10^4
4 x 10^2.81
2.81 × 10^-4
The number 2.814 can be expressed in scientific notation as 2.81 × 10.
To express the number 2.814 in scientific notation, we need to move the decimal point so that there is one non-zero digit to the left of it. In this case, the decimal point needs to be moved two places to the left.
Therefore, the number 2.814 in scientific notation is 2.81 × 10.
To determine the number 2.814 in scientific notation, we need to express it as a number between 1 and 10, multiplied by a power of 10.
There are two ways to achieve this:
1) Move the decimal point to the left until a number between 1 and 10 is obtained. Count the number of places moved, which will be the exponent of 10.
2) Move the decimal point to the right until a number between 1 and 10 is obtained. Count the number of places moved, remembering that the exponent will be negative.
In this case, we need to move the decimal point to the right.
Starting with 2.814, we move one place to the right to get 28.14. From this, we can observe that moving two more places to the right will give us 281.4, which is a number between 1 and 10. Counting the number of places moved, we obtain an exponent of 10³=1000. However, since we moved the decimal point to the right, the exponent will be negative.
Therefore, the number 2.814 in scientific notation is 2.814 × 10^-3.