Question

Multiply the following numbers by moving the decimal. \(2.34 \times 10=\) ______

Short answer

23.4

Step-by-step solution

Understand the Problem

We need to multiply the number 2.34 by 10 by moving the decimal point.

Move the Decimal Point

Multiplying by 10 means you move the decimal point one place to the right. For 2.34, the decimal is between 2 and 3.

Perform the Calculation

When the decimal point in 2.34 is moved one place to the right, it becomes 23.4.

Verify the Result

Check that moving the decimal point one place to the right transforms 2.34 into 23.4. This confirms our multiplication is correct.

Key concepts

Understanding Place Value

Place value is a fundamental part of understanding numbers. Each digit in a number has a specific place value, based on its position relative to the decimal point. When dealing with decimal numbers, it's important to know that:

• The digit immediately to the left of the decimal point is the ones place.
• The next digit to the right is the tenths place.
• Further right, you have the hundredths, thousandths, and so on.

This concept helps us perform operations like multiplying decimals. By understanding place value, you can easily comprehend how moving a number left or right changes the number's meaning. For example, in the number 2.34, the '2' is in the ones place, the '3' is in the tenths place, and the '4' is in the hundredths place. When multiplying by a power of ten, like 10, each digit shifts right across place values.

Role of the Decimal Point

The decimal point plays a critical role in distinguishing the whole number part from the fractional part of a number. In decimal multiplication, especially by factors of ten, the decimal point's position dictates the outcome of the operation.

You can think about multiplying by 10 as a way to make a number ten times larger. This is achieved by moving the decimal point one place to the right. For instance, moving the decimal point in 2.34 one space to the right renders it 23.4, which illustrates an increase in size by a factor of ten.

• Multiplying by 100 moves it two places.
• Multiplying by 1000 moves it three places, and so on.

This systematic approach applies to all numbers, whether they are integers or decimals. Grasping this movement of the point is essential in pacing up calculations without undergoing lengthy multiplication steps.

Basics of Arithmetic Operations with Decimals

Basic arithmetic includes operations such as addition, subtraction, multiplication, and division. These operations become slightly more intricate when decimals are involved due to the decimal point.

Multiplication of decimals, as illustrated in the exercise, often involves simplifying the process via moving the decimal point. This step is more about understanding how the number amplifies rather than performing complex arithmetic.

Consider these points to simplify arithmetic with decimals:

• Align numbers by the decimal point for addition and subtraction.
• When multiplying by 10, 100, or another power of ten, only move the decimal point to simplify the calculation.
• For division, adjust the divisor to be a whole number if necessary to ease the calculation.

Engaging with arithmetic helps reinforce the knowledge of how decimals react under each operation. With practice, speed and efficiency in solving such mathematical problems will greatly improve.