You are solving a measurement problem where the numbers 2.09 × 109 and 4.053 × 10−4 are divided. How many significant digits should the quotient have?
a) 4
b) 3
c) 2
d) 1
The number of significant digits in the quotient of a division is determined by the number with the least significant digits used in the division.
In this case, the number 4.053 × 10^(-4) has 4 significant digits, while the number 2.09 × 10^9 has only 3 significant digits.
Thus, the quotient should have 3 significant digits.
The correct answer is: b) 3
To determine how many significant digits the quotient should have, we need to count the number of significant digits in the numbers being divided.
In 2.09 × 10^9, there are 3 significant digits (2, 0, and 9). The exponent, 9, does not count as a significant digit.
In 4.053 × 10^-4, there are 4 significant digits (4, 0, 5, and 3). The exponent, -4, does not count as a significant digit.
When dividing two numbers, the result should have the same number of significant digits as the number with the fewest significant digits. Therefore, the quotient should have 3 significant digits, as that is the number of significant digits in 2.09 × 10^9.
Therefore, the answer is b) 3.
To determine the significant digits in the quotient, you need to follow a specific set of rules:
1. Count the number of significant digits in each of the numbers being divided.
For the number 2.09 × 10^9, there are three significant digits: 2, 0, and 9.
For the number 4.053 × 10^-4, there are four significant digits: 4, 0, 5, and 3.
2. Divide the two numbers as you normally would.
2.09 × 10^9 / 4.053 × 10^-4 = 515440.209
3. Determine the number of significant digits in the resulting quotient.
Since the number with the fewest significant digits is the number 4.053 × 10^-4 with four significant digits, it determines the number of significant digits in the final quotient.
Therefore, the quotient should have four significant digits.
The correct answer is:
a) 4