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Chapter 0: Problem 49

\(23.29 \div 1000\)

Short Answer

Expert verified
0.02329

Step by step solution

01

Understand the Division

The goal is to divide the number 23.29 by 1000. This can be done by shifting the decimal point of 23.29 three places to the left, since we are dividing by a power of 10.
02

Shift the Decimal Point

Move the decimal point in 23.29 three places to the left. Start at its current position between the 3 and the 2, move it three places to the left.
03

Write the New Number

After moving the decimal point three places to the left, we get 0.02329.
04

Verify the Result

Double-check that moving the decimal point is equivalent to dividing by 1000. In this case, 23.29 divided by 1000 is indeed 0.02329.

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Key Concepts

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

decimal point
Understanding the decimal point is crucial in decimal division. A decimal point separates the whole number part from the fractional part of a number. For example, in 23.29, the number 23 is the whole number part, and 29 is the fractional part.
When you divide by powers of ten, the position of the decimal point determines the outcome of the division. Moving the decimal point to the left makes the number smaller.
Let's practice: If you divide 5.67 by 10, the decimal point moves one place to the left, making the result 0.567. Notice how shifting the decimal changes the number.
division by powers of ten
When dividing by powers of ten, you shift the decimal point to the left by as many places as the number of zeros in the power of ten.
For instance, dividing by 10 shifts it one place, by 100 shifts it two places, and by 1000 moves it three places. In our exercise, we're dividing 23.29 by 1000.
Since 1000 has three zeros, we move the decimal point three places to the left. Thus, 23.29 becomes 0.02329.
Simple rule: For every zero in the divisor (like 100, 1000), move the decimal left by that many places.
step-by-step solution
Let's break down our exercise in a step-by-step manner to understand how we reached the solution.
Step 1: Recognize the task: We need to divide 23.29 by 1000. Understanding that this involves shifting the decimal point leftward is key.
Step 2: Move the decimal: Starting with 23.29, move the decimal point three places to the left. Since 23.29 already has the decimal after the 3, you'd move it past 2, then 3, filling in with zero if needed.
Step 3: Result: The number transforms from 23.29 into 0.02329.
Step 4: Verification: Always double-check your result. Ensure your decimal shift was correct. Dividing 23.29 by 1000 should indeed give you 0.02329.

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