Multiply or divide as indicated. 12.8 × 9.1

Verified step by step guidance

1. Identify the operation: The problem asks to multiply 12.8 by 9.1.
2. Write the multiplication expression as \$12.8 \times 9.1$.
3. Ignore the decimal points initially and multiply the numbers as if they were whole numbers: multiply 128 by 91.
4. Count the total number of decimal places in both original numbers. Here, 12.8 has 1 decimal place and 9.1 has 1 decimal place, so total decimal places = 2.
5. After multiplying the whole numbers, place the decimal point in the product so that it has 2 decimal places, matching the total from step 4.

Key Concepts

Multiplication of Decimal Numbers

Multiplying decimal numbers involves treating them as whole numbers first, then placing the decimal point in the product. The total number of decimal places in the factors determines the decimal places in the answer. For example, multiplying 12.8 by 9.1 requires counting decimal digits and adjusting the product accordingly.

Place Value and Decimal Points

Understanding place value is essential when working with decimals. Each digit's position relative to the decimal point determines its value. Correctly positioning the decimal point after multiplication ensures the product reflects the true value of the numbers involved.

Order of Operations and Arithmetic Procedures

Following the correct arithmetic procedures, such as multiplication before division, ensures accurate results. In this problem, since only multiplication is involved, performing the operation directly and carefully is key to obtaining the correct product.