8.03 ✕ 10v-8 - 2.56 ✕ 10v-2 show your work
To simplify the expression 8.03 ✕ 10^(-8) - 2.56 ✕ 10^(-2), we can write it as:
(8.03 / 10^8) - (2.56 / 10^2)
= (8.03 / 100000000) - (2.56 / 100)
= 0.0000000803 - 0.0256
= -0.0255999197
To subtract two numbers written in scientific notation, we need to ensure that the exponents of the powers of 10 are the same. Here's the step-by-step solution:
1. Convert both numbers to scientific notation if they are not already in that form.
8.03 × 10^(-8) - 2.56 × 10^(-2)
2. Rewrite the numbers with the same exponent by adjusting the decimal places.
8.03 × 10^(-8) = 0.0000000803 × 10^0
2.56 × 10^(-2) = 0.0256 × 10^0
3. Now, we can directly subtract the significands (the numbers in front of the powers of 10).
0.0000000803 - 0.0256 = -0.0255
4. Keep the common exponent, which is 10^0.
So, the final result is -0.0255 × 10^0 or just -0.0255.
To subtract these two numbers written in scientific notation, we need to have the same exponent (v) for both numbers. In this case, we have 10 raised to different exponents: -8 and -2.
To make the exponents the same, we can rewrite 8.03 × 10^(-8) as a number with an exponent of -2. This can be achieved by moving the decimal point to the right by six places:
8.03 × 10^(-8) = 0.00000803 × 10^(-2)
Now that the exponents are the same, we can subtract the numbers:
0.00000803 × 10^(-2) - 2.56 × 10^(-2)
To subtract these numbers, we only need to consider the decimal parts since the exponents are the same. Hence, we get:
0.00000803 - 2.56 = -2.55999197
Now we can write the result in scientific notation. Since the decimal part is negative, we need to move the decimal point to the left by one place, and the exponent is raised by one:
-2.55999197 = -0.255999197 × 10^1
Therefore, the subtraction of 8.03 × 10^(-8) minus 2.56 × 10^(-2) is equal to -0.255999197 × 10^1, or approximately -2.56.