Evaluate (2.1 x 10^4) + (5.68 x 10^-2)Express the result in standard form.
Can you explain your steps? I don't understand how to solve this with the negative 2
21000 + .0568
When something is raised to a negative power, (in this case 10 raised to -2), it means you have to take the reciprocal of the given number and then raise it to the positive power.
For example,
10^-2 = (1/10)^2 = (1/100) = 0.01
2^-4 = (1/2)^4 = 1/16
In this question,
(2.1 x 10^4) + (5.68 x 10^-2)
= 21000 + 0.0568
= 21000.0568
The second number is really tiny compared to the first, so you could still note it as 2.1 x 10^4. If you'd like to be more precise, you have your answer (21000.0568) which can be converted to standard form.
To evaluate the expression (2.1 x 10^4) + (5.68 x 10^-2), we need to add the two numbers together. However, we first need to express them in the same power of 10.
The number 2.1 x 10^4 is already in standard form, which means the decimal point is after the first digit.
To express 5.68 x 10^-2 in standard form, we need to move the decimal point two places to the left because the exponent is negative. This gives us 0.0568 x 10^0.
Now, we can add the two numbers together:
(2.1 x 10^4) + (0.0568 x 10^0)
Since the exponent of 10 is the same for both numbers (4 and 0), we can add the coefficients (2.1 and 0.0568) directly:
2.1 + 0.0568 = 2.1568
Finally, we express the result in standard form by moving the decimal point to the right until there is only one nonzero digit to the left of the decimal point. In this case, the result is already in standard form:
2.1568 x 10^4
To solve this problem, we need to add two numbers written in scientific notation.
The first number is 2.1 multiplied by 10 raised to the power of 4, represented as 2.1 x 10^4.
The second number is 5.68 multiplied by 10 raised to the power of -2, represented as 5.68 x 10^-2.
To add these numbers, we must make sure that they have the same exponent. We can achieve this by manipulating the second number, so it has the same exponent as the first number.
In the case of the second number, we have 5.68 x 10^-2. To make it have an exponent of 4, we need to shift the decimal point to the right by two places. By doing so, we get 0.0568 x 10^4.
Now, we can simply add the two numbers:
2.1 x 10^4 + 0.0568 x 10^4 = 2.1568 x 10^4
To express the result in standard form, we write it as a decimal multiplied by a power of 10 without using scientific notation. In this case, it will be:
2.1568 x 10^4 = 21,568
So, the result in standard form is 21,568.