Question

Find each quantity without using a calculator. \(7.7 \div 1,000\)

Short answer

0.0077

Step-by-step solution

Understand Division by 1,000

Dividing a number by 1,000 means you move the decimal point three places to the left. This is because 1,000 has three zeros.

Identify the Decimal Point in 7.7

In the number 7.7, the decimal point is between 7 and 7.

Move the Decimal Point

Move the decimal point three places to the left. Since the original number is 7.7: First move: 0.77Second move: 0.077Third move: 0.0077

Write the Result

After moving the decimal point three places to the left, the result is 0.0077.

Key concepts

decimal point

A decimal point is a small dot (.) used to separate the whole number part from the fractional part of a number. In our example, the number 7.7 has a decimal point between the whole number 7 and the fraction 0.7.

Understanding the position of the decimal point is crucial in arithmetic operations, especially in division. Each movement of the decimal point to the left or right changes the number's value by an order of ten.

When dividing by powers of ten, like 10, 100, or 1,000, each power of ten moves the decimal point one more place to the left. For instance, dividing by 10 moves the decimal one place to the left, dividing by 100 moves it two places, and dividing by 1,000 shifts it three places.

division without calculator

Dividing numbers without a calculator builds a strong understanding of number relationships and place value. Let's discuss how to perform the division of 7.7 by 1,000 manually.

• First, recognize that dividing by 1,000 involves three decimal place movements to the left.
• Start with the number 7.7. Notice the decimal point sits between 7 (whole number) and 7 (fractional part).
• To divide 7.7 by 1,000, move the decimal point three positions to the left:
• First move: 0.77
• Second move: 0.077
• Third move: 0.0077

After three moves, you get the final result: 0.0077. This method helps ensure accuracy and reinforces why the movement of the decimal is significant when dividing by large numbers.

mathematics problem-solving

Mathematics problem-solving is about understanding and applying mathematical concepts to find answers. For our example, the systematic approach is crucial.

Here's a more detailed breakdown:

• Understand the problem: You need to find the result of 7.7 divided by 1,000.
• Identify key concepts: Division, decimal points, and place value.
• Apply the method: Realize that dividing by 1,000 moves the decimal point three places left.
• Double-check: After each move, verify intermediate steps (0.77, 0.077, 0.0077).

By following an orderly process, solving mathematical problems becomes more manageable. Understanding the why and how behind each step builds confidence and improves your problem-solving skills. It is essential to practice these steps frequently to internalize the patterns and techniques.