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Chapter 1: Problem 30

Divide. $$ 127,000 \div 100 $$

Short Answer

Expert verified
1270

Step by step solution

01

- Understand Place Value

Recognize that dividing a number by 100 shifts the decimal point two places to the left.
02

- Identify the Decimal Point

The number 127,000 has an implied decimal point at the end. It can be written as 127,000.0.
03

- Shift the Decimal Point

Shift the decimal point two places to the left. Moving the decimal point in 127,000.0 two places to the left gives 127,000.0 -> 1,270.00.
04

- Simplify

Remove any unnecessary zeros. The final value is 1,270.

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Key Concepts

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

place value
Place value is a fundamental concept in mathematics that helps us understand the value of digits in a number based on their position. Each position in a number has a different value. For instance, in the number 127,000, the digit '1' is in the hundred thousand place, '2' in the ten thousand place, '7' in the thousand place, and so forth.

When we divide by 100, we shift each digit two places to the right, effectively reducing each digit's value by a factor of 100. This process is crucial for solving division problems efficiently and accurately.
decimal point
The decimal point is a vital part of our number system, separating the whole number part from the fractional part. Understanding how to manipulate the decimal point can simplify many arithmetic operations, particularly division and multiplication by powers of 10.

In our given problem, 127,000 can be written with an implied decimal point as 127,000.0. When we divide by 100, we shift this decimal point two places to the left:

\[ 127000.0 \rightarrow 1270.00 \]

This shift makes it easier to see the new value of our number after division.
simplification
Simplification is the process of reducing a mathematical expression or number to its simplest form. This often involves eliminating unnecessary components, such as zeroes, or reducing fractions.

After shifting the decimal point in 127,000.0 two places to the left, we get 1270.00. Simplifying this entails removing the trailing zeros, resulting in 1270.

This step makes our final answer clean and easy to interpret. Simplifying results is a standard practice to ensure clarity and precision in mathematics.

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