What is the quotient of 9, point, 8, times, 10, to the power 79.8×10
7
and 7, point, 0, times, 10, to the power 47.0×10
4
expressed in scientific notation?
To express the given quotient in scientific notation, we start by finding the quotient of 9.8 times 10^79.8 divided by 7.0 times 10^47.0.
9.8 times 10^79.8 divided by 7.0 times 10^47.0 is equal to (9.8/7.0) times (10^79.8/10^47.0).
The quotient of 9.8 divided by 7.0 is approximately 1.4, while the quotient of 10^79.8 divided by 10^47.0 is equal to 10^(79.8-47.0) or 10^32.8.
Multiplying these two quotients together, we get 1.4 times 10^32.8.
Therefore, the quotient 9.8 times 10^79.8×10^7 divided by 7.0 times 10^47.0×10^4 expressed in scientific notation is approximately 1.4 times 10^32.8.
To find the quotient in scientific notation, we first need to evaluate the numbers separately and then divide them.
Let's evaluate the numerator, 9.8 times 10 to the power 79.8 times 10^7:
9.8 x 10^79.8 x 10^7
To multiply numbers in scientific notation, we can add the exponents and multiply the coefficients:
9.8 x 10^((79.8 + 7) * 10)
= 9.8 x 10^((86.8) * 10)
= 9.8 x 10^(868)
Now, let's evaluate the denominator, 7.0 times 10 to the power 47.0 times 10^4:
7.0 x 10^47.0 x 10^4
Following the same steps, we get:
7.0 x 10^((47.0 + 4) * 10)
= 7.0 x 10^((51.0) * 10)
= 7.0 x 10^(510)
Finally, we can divide the evaluated expressions:
(9.8 x 10^868) / (7.0 x 10^510)
To divide numbers in scientific notation, we divide the coefficients and subtract the exponents:
(9.8/7.0) x 10^(868-510)
= 1.4 x 10^358
Therefore, the quotient of (9.8 x 10^79.8 x 10^7) / (7.0 x 10^47.0 x 10^4) expressed in scientific notation is 1.4 x 10^358.
To find the quotient of two numbers expressed in scientific notation, we need to divide the coefficients and subtract the exponents.
Let's break it down step by step:
Step 1: Divide the coefficients.
The coefficient of the first number is 9.8 × 10^79.
The coefficient of the second number is 7.0 × 10^47.
Divide the coefficient of the first number by the coefficient of the second number:
9.8 ÷ 7.0 = 1.4
Step 2: Subtract the exponents.
The exponent of the first number is 79.8 × 10^7.
The exponent of the second number is 47.0 × 10^4.
Subtract the exponent of the second number from the exponent of the first number:
79.8 × 10^7 - 47.0 × 10^4 = 79.8 × 10^3
Step 3: Write the result in scientific notation.
Combine the quotient (1.4) and the new exponent (10^3):
1.4 × 10^3
Therefore, the quotient of 9.8 × 10^79.8 × 10^7 and 7.0 × 10^47.0 × 10^4 expressed in scientific notation is 1.4 × 10^3.