How much greater is 2, point, 6, times, 10, to the power minus 42.6×10
−4
than 5, point, 9, times, 10, to the power minus 55.9×10
−5
? Express your answer using either standard notation or scientific notation.
Answer
Attempt 1 out of 2
Standard Notation
Answer:
To answer this question, we need to subtract the second value from the first value.
2.6 times 10 to the power of -42.6x10^-4 is written as 2.6 x 10^(-42.6x10^-4)
5.9 times 10 to the power of -55.9x10^-5 is written as 5.9 x 10^(-55.9x10^-5)
To subtract these values, we need to subtract the coefficients (2.6 - 5.9) and subtract the exponents of 10 (-42.6x10^-4 - (-55.9x10^-5))
Simplifying the exponents:
-42.6x10^-4 + 55.9x10^-5 = -42.6 * 10^-4 + 55.9 * 10^-5 = (-42.6 - 5.59) * 10^-4 = -48.19*10^-4
Therefore, the difference is (2.6 - 5.9) times 10^(-48.19*10^-4) or -3.3 x 10^(-48.19*10^-4).
Expressing this in standard notation, the answer is -0.0000000000000000033.
To calculate how much greater 2.6 x 10^-4 is compared to 5.9 x 10^-5, we need to find the difference between the two numbers.
First, let's write both numbers in standard notation:
2.6 x 10^-4 = 0.00026
5.9 x 10^-5 = 0.000059
Now, subtract the smaller number from the larger number:
0.00026 - 0.000059 = 0.000201
Therefore, 2.6 x 10^-4 is 0.000201 greater than 5.9 x 10^-5.
To find the difference between these two numbers, you need to subtract them. The first number is 2.6 times 10 to the power of -42, and the second number is 5.9 times 10 to the power of -55.
Convert both numbers to standard form:
- For the first number, 2.6 times 10 to the power of -42 can be written as 2.6 x 10^-42
- For the second number, 5.9 times 10 to the power of -55 can be written as 5.9 x 10^-55
Subtract the second number from the first number:
(2.6 x 10^-42) - (5.9 x 10^-55)
To simplify this, you need to make the exponents the same by manipulating the numbers in the scientific notation. Since the exponent of the first number is -42 and the exponent of the second number is -55, you can write the second number as 0.59 x 10^-42.
Now you can subtract the two numbers:
(2.6 x 10^-42) - (0.59 x 10^-42)
Subtract the numbers outside of scientific notation: 2.6 - 0.59 = 2.01
Keep the exponent as -42 since it is the higher value among the two:
2.01 x 10^-42.
So, the difference between 2.6 times 10 to the power of -42 and 5.9 times 10 to the power of -55 is approximately 2.01 times 10 to the power of -42.