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Chapter 5: Problem 59

Divide by the powers of 10. $$1.02 \div 1000$$

Short Answer

Expert verified
0.00102

Step by step solution

01

- Understand the Problem

Identify the numbers involved in the division problem. The task is to divide 1.02 by 1000.
02

- Recognize the Division by Powers of 10

Understand that dividing by powers of 10 (such as 10, 100, 1000) involves moving the decimal point to the left. For 1000, you need to move the decimal point three places to the left.
03

- Move the Decimal Point

Starting with 1.02, move the decimal point three places to the left. Moving once: 0.102Moving twice: 0.0102Moving three times: 0.00102.
04

- Write the Final Answer

The result of dividing 1.02 by 1000 is 0.00102.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Decimal Point
To grasp the concept of dividing by powers of 10, one must understand what a decimal point is. The decimal point is a dot used to separate the whole number part from the fractional part of a number. For instance, in 1.02, the decimal point separates 1 (the whole number part) from 02 (the fractional part). When you divide by powers of 10, the position of this decimal point will change.
Division
Division is a mathematical operation where you split a number into equal parts. When you divide a number, you essentially find out how many times one number is contained within another. In this exercise, you are dividing 1.02 by 1000. The key aspect to remember here is that division by powers of 10 simplifies due to the unique properties of the decimal system.
Powers of 10
Powers of 10 are numbers like 10, 100, 1000, and so on. The 'power' tells you how many times to multiply 10 by itself. For instance, 10^1 is 10, 10^2 is 100, and 10^3 is 1000. When dividing by a power of 10, the operation is simplified by just moving the decimal point. The number of places you move the decimal point is determined by the power of 10 you are dividing by. For instance, dividing by 1000 (which is 10^3) means moving the decimal three places to the left.
Step by Step Solution
Now let's apply this understanding in a step-by-step solution to the problem of dividing 1.02 by 1000.

Step 1 - Understand the Problem: Identify that you need to divide 1.02 by 1000.

Step 2 - Recognize the Division by Powers of 10: Note that 1000 is a power of 10 (10^3), which means you'll move the decimal point three places to the left.

Step 3 - Move the Decimal Point: Start with the number 1.02.
  • Move the decimal once: 0.102
  • Move it a second time: 0.0102
  • Move it a third time: 0.00102
So, 1.02 divided by 1000 is 0.00102.

Step 4 - Write the Final Answer: The result of this division is 0.00102.

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