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Chapter 6: Problem 37

Perform each operation and simplify. $$ 150.79 \div 100 $$

Short Answer

Expert verified
1.5079

Step by step solution

01

Understand the Operation

We need to divide 150.79 by 100. Division by 100 essentially moves the decimal point two places to the left in the number.
02

Shift the Decimal Point

Start with the number 150.79. Move the decimal point two places to the left. This means we count two digits towards the left of the decimal point.
03

Apply the Shift

Move the decimal point from 150.79 to get 1.5079. Since we are moving two places left, we place the decimal after the digit 1.
04

Confirm and Simplify

The resulting number after moving the decimal is 1.5079. There is no further simplification needed.

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Key Concepts

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

Understanding Decimal Points in Division
When you encounter division by powers of ten, such as 100, you'll often deal with moving the decimal point. Knowing how to shift the decimal point simplifies complex mathematical operations and is a valuable skill. In our case, starting with 150.79 and dividing by 100 means you move the decimal point two places to the left. Why two places? Because 100 has two zeros. Each zero represents a step to the left for the decimal. Let's visualize this:
  • Start at 150.79 (the decimal is after the 150).
  • Move one spot to get 15.079.
  • Move a second spot to get 1.5079.
Now, you've successfully divided by 100, transforming 150.79 into 1.5079 by simply relocating the decimal point.
Simplifying Fractions After Division
Fractions represent division and often need simplification for better interpretation. However, sometimes division won't require further fraction simplification, as seen in 150.79 divided by 100. Once you've shifted the decimal and arrived at 1.5079, re-evaluate if the number can be simplified further. This check ensures clarity and precision:
  • In this instance, we have no fractional form to reduce because our result is a decimal, 1.5079.
  • If a fraction appears, break it down to its simplest form by finding the greatest common divisor (GCD) of the numerator and denominator. Divide both by this GCD to simplify.
Where no further fractions emerge, as is the case, your work is complete.
Navigating Mathematical Operations with Ease
Mathematical operations often seem tricky, but breaking them down step-by-step eases the process significantly. Let鈥檚 consider the operation from the division problem you solved. Start simple:
  • Identify the operation: Here, it's dividing 150.79 by 100.
  • Understand the relationship: Division by a factor of 10 shifts decimals, simplifying operations like 150.79 梅 100 to 1.5079 effortlessly.
  • Combine skills learned: Apply understanding of decimals and fractions, as seen in converting 150.79 directly to a simpler form without complex calculations.
This approach not only simplifies division but builds confidence in handling mathematical problems efficiently.

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Most popular questions from this chapter

Write each decimal fraction. One and ten ten-millionths.

Convert each fraction or complex decimal number to a decimal (in which no proper fractions appear). \(5.66 \frac{2}{3}\)

Use a calculator to convert each fraction to a decimal. If no repeating pattern seems to exist, round to four decimal places. \(\frac{85}{311}\)

Find each product and check each result with a calculator. \(6.1 \cdot 7\)

Perform each operation. $$ 0.21387 \div 0.19 $$
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