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Chapter 1: Problem 31

Divide. $$ 127,000 \div 1000 $$

Short Answer

Expert verified
The result is 127.

Step by step solution

01

- Understand the division

The problem requires dividing 127,000 by 1,000. When dividing by 1,000, you are essentially determining how many times 1,000 fits into 127,000.
02

- Simplify using place value

Dividing by 1,000 can be simplified by moving the decimal point three places to the left. This is because 1,000 has three zeros.
03

- Move the decimal point

Start with 127,000. The decimal point is currently at the end of the number (127,000.0). Move the decimal point three places to the left: 127,000.0 -> 127.000
04

- Write the result

After moving the decimal point, the result is 127. So, 127,000 divided by 1,000 is 127.

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Key Concepts

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

Decimal Point Movement
To divide by powers of ten, we often shift the decimal point. Consider the number 127,000. The decimal point is at the end. When we divide 127,000 by 1,000, we move the decimal point to the left. Since 1,000 has three zeros, we move the decimal point three places to the left. This means that 127,000.0 becomes 127.000. Thus, moving the decimal point helps simplify the division process.
Place Value
Understanding place value is essential in division and other math operations. Each digit in a number has a value based on its position. For example, in 127,000, '1' stands for one hundred thousand, '2' stands for twenty thousand, and so forth. When dividing by powers of ten, like 1,000, you shift these values. Moving three places to the left changes '100,000' to '100'. This understanding aids in quick calculations.
Dividing By Powers of Ten
Dividing by powers of ten is a common and straightforward process in mathematics. Powers of ten include numbers like 10, 100, 1,000, and 10,000. When dividing by these, you shift the decimal point left by a number of places equal to the number of zeros. For instance, dividing by 10 moves it one place; by 100, two places. This technique simplifies calculations considerably.

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