Perform the indicated operation and write the answer in decimal notation.(3×103)(1.3×102)(3\$$times10^3)(1.3$$\$$times10^2)$$

Ch. P - Fundamental Concepts of Algebra

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

All textbooks

Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

Problem 36

Chapter 1, Problem 36

Perform the indicated operation and write the answer in decimal notation. $(3 \times 10^{3}) (1.3 \times 10^{2})$

Verified step by step guidance

Identify the given expression: $ (3 \times 10^{3}) (1.3 \times 10^{2}) $. This is a multiplication of two numbers expressed in scientific notation.

Use the property of exponents and multiplication: when multiplying numbers in scientific notation, multiply the coefficients (the numbers in front) and add the exponents of 10. So, multiply 3 and 1.3, and add the exponents 3 and 2.

Calculate the product of the coefficients: $3 \times 1.3$.

Add the exponents of 10: $3 + 2$ to get the new exponent.

Combine the results to write the product in scientific notation, then convert this scientific notation to decimal notation by moving the decimal point according to the exponent.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Scientific Notation

Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10. It simplifies working with very large or small numbers by using exponents, such as 3 × 10^3 representing 3000.

Multiplication of Numbers in Scientific Notation

When multiplying numbers in scientific notation, multiply the decimal parts and add the exponents of 10. For example, (3 × 10^3)(1.3 × 10^2) equals (3 × 1.3) × 10^(3+2).

Conversion to Decimal Notation

After performing operations in scientific notation, convert the result to decimal notation by calculating the power of 10 and multiplying it by the decimal number. This gives the final answer in standard numerical form.

Recommended video:

05:18

Interval Notation

Related Practice

Textbook Question

Add or subtract terms whenever possible. $4$\sqrt{13x}$ - 6$\sqrt{13x}$$

Textbook Question

List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. {-9, -4/5, 0, 0.25, √3, 9.2, √100}

Textbook Question

Find each product. (5−7x)(5+7x)

views

Textbook Question

Simplify each exponential expression in Exercises 23–64. $x^{14} / x^{7}$

Textbook Question

In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. 3x²+4xy+y²

Textbook Question

In Exercises 15–58, find each product. (4x²+5x)(4x²−5x)

views