What is the quotient of 4, point, 6, 5, 3, times, 10, to the power 74.653×10
7
and 7, point, 0, 5, times, 10, cubed7.05×10
3
expressed in scientific notation?
To find the quotient of 4.65 × 10^74.653 × 10^7 and 7.05 × 10^3 in scientific notation, follow these steps:
Step 1: Divide the coefficients: 4.65 ÷ 7.05 = 0.6595744681
Step 2: Subtract the exponent of the denominator from the exponent of the numerator: (10^74.653) - (10^3) = 10^(74.653 - 3) = 10^(71.653)
Step 3: Put the results together: 0.6595744681 × 10^71.653
The quotient in scientific notation is approximately 0.6595744681 × 10^71.653.
To calculate the quotient of two numbers expressed in scientific notation, you need to follow these steps:
Step 1: Convert the numbers to standard form.
- The first number, 4.65 × 10^7, can be converted to standard form by moving the decimal point 7 places to the right: 46,500,000.
- The second number, 7.05 × 10^3, can be converted to standard form by moving the decimal point 3 places to the right: 7,050.
Step 2: Divide the first number by the second number.
- Divide 46,500,000 by 7,050 to get 6,572.3404255 (approximately).
Step 3: Convert the result back to scientific notation.
To express a number in scientific notation, you need to rewrite it as a decimal number between 1 and 10, multiplied by a power of 10.
With the result, 6,572.3404255, you can express it in scientific notation as follows:
- Move the decimal point until there is only one non-zero digit to the left of the decimal point. In this case, it will be 6.5723404255.
- Count the number of places you moved the decimal point. It moved 4 places to the left.
- The final result in scientific notation is 6.5723404255 × 10^4.
Therefore, the quotient of 4.65 × 10^7 and 7.05 × 10^3, expressed in scientific notation, is approximately 6.572 × 10^4.
To calculate the quotient, divide the first number (4.653 × 10^74) by the second number (7.05 × 10^3).
Dividing 4.653 by 7.05 gives approximately 0.65957446809.
To calculate the exponent, subtract the exponent of the second number from the exponent of the first number.
74 - 3 = 71.
Therefore, the quotient can be expressed as (6.5957446809 × 10^71) in scientific notation.