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Chapter 5: Problem 60

Divide by the powers of 10. $$8.1 \div 1000$$

Short Answer

Expert verified
0.0081

Step by step solution

01

- Understanding the Problem

Start by identifying that the task is to divide 8.1 by 1000. This means you need to determine how many times 1000 can fit into 8.1 or what the quotient is when 8.1 is divided by 1000.
02

- Recognizing the Division by Power of 10

Recognize that dividing a number by 1000 (which is a power of 10: 10^3) involves moving the decimal point three places to the left.
03

- Move the Decimal Point

To divide 8.1 by 1000, move the decimal point three places to the left. Starting from 8.1, move the decimal point three places left: 8.1 鈫� 0.81 鈫� 0.081 鈫� 0.0081.
04

- Write the Result

After moving the decimal point, you obtain the final result: 0.0081.

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Key Concepts

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

Decimal Point Movement
One of the simplest ways to handle division by powers of 10 is to move the decimal point. For instance, in the problem, we need to divide 8.1 by 1000.

Whenever you divide by a power of 10, the number of zeros in the power of 10 tells you how many places to move the decimal point. In this case, 1000 is represented as 103.

Because there are three zeros, we move the decimal point three places to the left. So, starting with 8.1, we get:
  • Step 1: 8.1 鈫� 0.81
  • Step 2: 0.81 鈫� 0.081
  • Step 3: 0.081 鈫� 0.0081
Moving the decimal point makes the calculation much simpler. It is easier compared to doing long division.
Quotient Calculation
A quotient represents how many times the divisor fits into the dividend. In this case, we want to understand how many times 1000 goes into 8.1.

When you divide by powers of 10, quotient calculation becomes straightforward due to the easy movement of the decimal point. Instead of breaking down the long division manually, simply moving the decimal effectively computes the quotient.

For instance, dividing 8.1 by 1000, as shown before, results directly in the value of the quotient being 0.0081.

You can always verify by multiplying the quotient back with the divisor to see if you get the original number. Thus, 0.0081 multiplied by 1000 gives you back 8.1, confirming the answer.
Powers of 10
Understanding what powers of 10 mean is crucial when performing related calculations. A power of 10 simply indicates how many times 10 is multiplied by itself.

For example, 1000 can be written as 103, which means 10 脳 10 脳 10. Every additional power of 10 adds one zero.

When dividing or multiplying by powers of 10:
  • Dividing by 10n (where n is a positive integer) moves the decimal point n places to the left.
  • Multiplying by 10n moves the decimal point n places to the right.
Understanding this base concept helps in both simplifying and verifying calculations involving large or small numbers.

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