Question

Solve the following. Carry division to the hundredths place where necessary. \(0.15 \times 100=\) ______

Short answer

15.00

Step-by-step solution

Understand the Problem

We need to multiply the decimal number 0.15 by 100 and find its product. Since we are tasked with division to the hundredths, ensuring decimal precision is key.

Perform the Multiplication

To multiply 0.15 by 100, you'll shift the decimal place two spaces to the right (because 100 has two zeros). Thus, 0.15 becomes 15.00. In mathematical terms, \(0.15 \times 100 = 15.00\).

Verify the Result

Let's confirm our calculation by considering the logic of multiplying by 100. Multiplying a decimal by 100 effectively scales it by 100 times, achieving what we initially determined, which is 15.00.

Key concepts

Place Value

Understanding place value is crucial when working with decimals. Place value refers to the position of a digit within a number. For example, in the decimal number 0.15, '1' is in the tenths place, and '5' is in the hundredths place. Each position has a value ten times that of the position to its right. This concept helps you understand the magnitude of numbers and how they change as they move through different decimal places.
When multiplying 0.15 by 100, we can see this change in place value. The decimal point is moved two places to the right, converting the number into 15.00. It's essential to grasp this idea, as it ensures you correctly adjust the number based on the multiplication, maintaining its true value. Knowing the correct place value for each digit in a decimal helps prevent errors in arithmetic operations.

Mathematical Procedures

Mathematical procedures guide you on how to approach and solve problems methodically. For decimal multiplication, you follow a specific procedure to ensure accuracy. First, identify the number of zeros in the multiplier, in this case, 100, which has two zeros. This informs you that you will move the decimal point two places.
Next, you execute the procedure of shifting the decimal point of the number, 0.15, two places to the right. It's important to keep track of these shifts to ensure precision. After shifting, you add zeros to the end if necessary to maintain the number's structure.

• Recognize the operation needed clearly—here, multiplication of a decimal by a whole number.
• Identify any necessary shifts based on the number of zeros in the multiplier.
• Execute the operation and double-check the final placement of the decimal.

By following these steps, you ensure a systematic approach that minimizes the chance of errors.

Arithmetic Operations

Arithmetic operations include the basic mathematical functions such as addition, subtraction, multiplication, and division. Decimal multiplication, like in this case, is a core aspect of arithmetic operations. To effectively multiply a decimal by a whole number, an understanding of both the operation itself and the decimal system is necessary.
In decimal multiplication, the key is to shift the decimal point the appropriate number of places in accordance with the multiplier. This is straightforward when working with powers of ten, such as 10, 100, or 1000. For example, when multiplying 0.15 by 100, you shift the decimal two places, resulting in the product 15.00.
This operation highlights how multiplication affects decimal numbers, and underscores the importance of accurately shifting the decimal point instead of performing traditional multiplication, ensuring the number's magnitude changes correctly.