Question

Estimate the product of 4,308,229 and 44 to one significant figure (show your work and do not use a calculator), and express the result in standard scientific notation.

Short answer

Question: Estimate the product of 4,308,229 and 44 to one significant figure and express the result in standard scientific notation. Answer: 1.6 × 10^8

Step-by-step solution

Round the numbers to one significant figure

First, we will round the given numbers to one significant figure. To do this, we will consider the first non-zero digit of each number and any digit that follows it. For 4,308,229: The first non-zero digit is 4, and the following digit is 3. Since 3 is less than 5, we will round down and get 4,000,000. For 44: The first non-zero digit is 4, and the following digit is also 4. Since the following digit is 4, which is less than 5, we will round down and get 40.

Multiply the rounded numbers

Next, we will multiply the two numbers that we rounded in the previous step: 4,000,000 and 40. Product = 4,000,000 × 40 = 160,000,000

Express the result in standard scientific notation

Finally, we will express the result, which is 160,000,000, in standard scientific notation. To do this, we will write the number as a product of a number between 1 and 10 and a power of 10. 160,000,000 = 1.6 × 10^8 So, the estimated product of 4,308,229 and 44 to one significant figure is 1.6 × 10^8 in standard scientific notation.