Last Year, A Large Trucking Company Delivered $9.5 \times 10^5$ Tons Of Goods With An Average Value Of $20,000 Per Ton. What Was The Total Value Of The Goods Delivered? Write The Answer In Scientific Notation.A. $1.9 \times 10^{10}$

**Calculating the Total Value of Goods Delivered: A Step-by-Step Guide**

What is the total value of goods delivered by the trucking company?

To find the total value of goods delivered, we need to multiply the number of tons delivered by the average value per ton.

Step 1: Understand the given values

• Number of tons delivered: $9.5 \times 10^5$
• Average value per ton: $20,000$

Step 2: Multiply the number of tons by the average value per ton

To multiply these two values, we need to multiply the coefficients ($9.5$ and $20,000$) and add the exponents ($10^5$ and $10^4$).

Multiplying the coefficients

$9.5 \times 20,000 = 190,000$

Adding the exponents

$10^5 \times 10^4 = 10^{5+4} = 10^9$

Combining the results

$190,000 \times 10^9 = 1.9 \times 10^{10}$

What is the total value of goods delivered in scientific notation?

The total value of goods delivered is $1.9 \times 10^{10}$.

Q: What is the significance of scientific notation in this problem?

A: Scientific notation is a way of expressing very large or very small numbers in a compact form. In this problem, we used scientific notation to express the number of tons delivered ($9.5 \times 10^5$) and the total value of goods delivered ($1.9 \times 10^{10}$). This makes it easier to understand and work with these large numbers.

Q: How do I convert a number from standard notation to scientific notation?

A: To convert a number from standard notation to scientific notation, you need to move the decimal point to the left or right until you have a number between $1$ and $10$. Then, multiply the number by $10$ raised to the power of the number of places you moved the decimal point.

Q: What is the difference between standard notation and scientific notation?

A: Standard notation is a way of expressing numbers in their usual form, with a decimal point and a whole number part. Scientific notation is a way of expressing numbers in a compact form, with a coefficient between $1$ and $10$ and an exponent of $10$.

Q: When should I use scientific notation?

A: You should use scientific notation when working with very large or very small numbers, such as numbers in the millions, billions, or trillions. Scientific notation makes it easier to understand and work with these large numbers.

Q: How do I add or subtract numbers in scientific notation?

A: To add or subtract numbers in scientific notation, you need to add or subtract the coefficients and add or subtract the exponents. For example, if you have $2.5 \times 10^3$ and $3.2 \times 10^3$, you would add the coefficients ($2.5 + 3.2 = 5.7$) and add the exponents ($10^3 + 10^3 = 10^6$), resulting in $5.7 \times 10^6$.

Q: How do I multiply or divide numbers in scientific notation?

A: To multiply or divide numbers in scientific notation, you need to multiply or divide the coefficients and add or subtract the exponents. For example, if you have $2.5 \times 10^3$ and $3.2 \times 10^4$, you would multiply the coefficients ($2.5 \times 3.2 = 8$) and add the exponents ($10^3 + 10^4 = 10^7$), resulting in $8 \times 10^7$.