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Chapter 0: Problem 50

\(59.8 \div 1000\)

Short Answer

Expert verified
0.0598

Step by step solution

01

Understand the Division

Recognize that the division problem requires dividing 59.8 by 1000. This means we need to find how many times 1000 fits into 59.8 or essentially shift the decimal point.
02

Shift the Decimal Point

To divide by 1000, shift the decimal point three places to the left. In 59.8, the decimal is after 9.
03

Perform the Division

Move the decimal point three places to the left. Starting from 59.8, the new position of the decimal point is 0.0598.

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Key Concepts

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

Shifting Decimal Points
Decimal division often involves shifting decimal points, a process that simplifies calculations.
When you divide a number with decimals by another number, you can adjust the decimal point to make the division easier.

For example, to divide 59.8 by 1000, you are essentially shifting the decimal point to the left:
  • Start with 59.8 and notice the decimal point after 9.
  • Shift the decimal three places to the left for 1000.
  • The result is 0.0598.
This method helps you avoid manual long division and quickly gives you the correct answer.
Division by Powers of Ten
When you divide by powers of ten (like 10, 100, 1000), the calculation follows a simple rule.
Each power of ten corresponds to a movement in the decimal point:
  • Dividing by 10 means moving the decimal one place to the left.
  • Dividing by 100 means moving it two places to the left.
  • Dividing by 1000 means moving it three places to the left.

For example, dividing 59.8 by 1000:
  • Start with 59.8, where the decimal is after 9.
  • Shift the decimal three places to the left to reflect division by 1000.
  • The new position of the decimal point is 0.0598.
This simple shifting mechanism helps you understand the impact of dividing by powers of ten.
Place Value in Decimals
Understanding place value is crucial when dealing with decimals.
Each digit in a decimal number has a specific position and value:
  • In 59.8, the digit '5' is in the tens place, '9' is in the units place, and '8' is in the tenths place.

When you shift the decimal point during division, you also change the place values:
  • In our example, moving the decimal three places to the left from 59.8 to 0.0598 affects all place values.
  • The new number has '5' in the thousandths place, '9' in ten-thousandths place, and '8' in hundred-thousandths place.
Recognizing these changes helps you accurately perform decimal division and understand the significance of each digit in the result.

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Most popular questions from this chapter

Write each improper fraction as a mixed number. $$ \frac{101}{15} $$

Identify each number as prime, composite, or neither. If the number is composite, write it as a product of prime factors. $$ 138 $$

Find each product or quotient, and write it in lowest terms as needed. $$ \frac{2}{5} \div 30 $$

Identify each number as prime, composite, or neither. If the number is composite, write it as a product of prime factors. $$ 51 $$

\(0.2 \times 0.03\)
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