You are solving a measurement problem where the numbers 4.514 x 10−3, 3.09 x 107, and 2.80 x 103 are multiplied. How many significant digits should the product have?
a) 1
b) 2
c) 3
d) 4
To determine the number of significant digits in the product, we need to consider the rules for multiplying numbers with significant figures:
- When multiplying numbers, count the significant figures in each number being multiplied and choose the smallest number of significant figures as the number of significant figures in the product.
Let's apply this rule to the given numbers:
4.514 x 10^(-3) has 4 significant figures
3.09 x 10^7 has 3 significant figures
2.80 x 10^3 has 3 significant figures
The smallest number of significant figures among the three numbers is 3. Therefore, the product should have 3 significant digits.
Therefore, the correct answer is c) 3.
To determine the number of significant digits in the product of these numbers, we need to follow the rules of significant figures.
1) When multiplying or dividing, the result should have the same number of significant digits as the measurement with the fewest significant digits.
2) In this case, the measurement with the fewest significant digits is 4.514 x 10^-3, which has 4 significant digits.
3) Thus, the product should have 4 significant digits.
Therefore, the correct answer is d) 4.
To determine the number of significant digits in the product of the given numbers, you need to follow the rules for significant digits when multiplying.
1. Multiply the numbers: 4.514 x 10−3 * 3.09 x 107 * 2.80 x 103
= (4.514 * 3.09 * 2.80) * (10−3 * 107 * 103)
2. Multiply the numerical values separately:
= 40.70344 * (10−3 * 107 * 103)
3. Perform the multiplication inside the parentheses:
= 40.70344 * (10−3 * 1010 * 103)
4. Simplify the exponent:
= 40.70344 * (10−3+1010+3)
= 40.70344 * 1010
= 41165.2224
The product of the given numbers is approximately 41165.2224.
The number of significant digits in the product is determined by the least number of significant digits in any of the factors. Let's check each factor:
- 4.514 x 10−3: This number has four significant digits.
- 3.09 x 107: This number has three significant digits.
- 2.80 x 103: This number has three significant digits.
The factor with the least number of significant digits is 3.09 x 107, which has three significant digits. Therefore, the product should also have three significant digits.
The answer is (c) 3 significant digits.