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Chapter 5: Problem 153

Evaluate. Express answers in standard notation. $$ \frac{0.05 \times 1600}{0.0004} $$

Short Answer

Expert verified
200,000

Step by step solution

01

- Multiply the Numerator

First, calculate the multiplication in the numerator: \(0.05 \times 1600\).
02

- Simplify the Numerator

Now solve the multiplication: \(0.05 \times 1600 = 80\).
03

- Divide by the Denominator

Next, divide the result from Step 2 by the denominator: \(\frac{80}{0.0004}\).
04

- Perform Division

Carry out the division: \(\frac{80}{0.0004} = 200,000\).
05

- Express in Standard Notation

The final answer in standard notation is: 200,000.

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Key Concepts

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

Numerator Multiplication
When dealing with fractions that involve decimals, the first step often involves multiplying the numbers in the numerator. In the exercise given, we need to multiply 0.05 by 1600.
Multiplying these two numbers together helps simplify the fraction and make the calculation easier as we move forward.
Here鈥檚 how we multiply decimals and whole numbers:
  • Align the numbers by their right-most digit when multiplying, ignoring the decimal points initially.
  • Multiply as if they are whole numbers: 5 x 1600 = 8000.
  • Next, count the total number of decimal places in the factors. In 0.05, there are two decimal places.
  • Place the decimal point in the product (8000) so that it has the same number of decimal places. Thus, 8000 becomes 80.0 or simply 80.
Therefore, multiplying the numerator 0.05 by 1600 gives us 80.
Denominator Division
The next important step is to divide the simplified numerator by the denominator. Here, we need to divide 80 by 0.0004.
Dividing by a decimal can seem tricky, but it becomes simple if we convert it into a whole number first. Here鈥檚 how:
  • Count the decimal places in 0.0004 (which is 4).
  • Move the decimal point 4 places to the right to turn it into the whole number 4.
  • Repeat the same shift in the numerator to balance out the fraction. Therefore, 80 becomes 800,000.
  • Now, divide as you would with whole numbers: 800,000 梅 4 = 200,000.
Thus, 80 divided by 0.0004 equals 200,000.
Standard Notation
Standard notation is a way of writing numbers so they are easily readable. It involves representing numbers without using exponents or scientific notation.
In our exercise, the final answer after performing the division is a large number: 200,000. This is already in standard notation.
However, understanding standard notation is crucial for accurately interpreting and expressing solutions. Here鈥檚 a quick reminder:
  • Standard notation writes numbers in their full decimal form without exponents.
  • Larger numbers can be written with commas to separate thousands, millions, etc., for better readability (e.g., 200,000).
  • No need for scientific notation unless specified or handling extremely large or small values.
This means our final answer is simply and clearly stated as 200,000.

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