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Chapter 4: Problem 42

Express answers in standard notation. $$ \frac{840,000 \times 0.03}{0.00021 \times 600} $$

Short Answer

Expert verified
200,000

Step by step solution

01

Calculate the Numerator

First, multiply the numbers in the numerator: \( 840,000 \times 0.03 = 25,200 \).
02

Calculate the Denominator

Next, multiply the numbers in the denominator: \( 0.00021 \times 600 = 0.126 \).
03

Divide the Numerator by the Denominator

Finally, divide the result of the numerator by the result of the denominator: \( \frac{25,200}{0.126} = 200,000 \).

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Key Concepts

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

Multiplication
Multiplication is one of the four basic arithmetic operations. It's essentially repeated addition. When you multiply two numbers, you're finding the total of one number taken multiple times. For example, in the exercise, we have the expression \(840,000 \times 0.03\).
Here鈥檚 how to understand it: you're adding 0.03 to itself 840,000 times! Here are some key ideas to help:
  • Always line up the numbers by their place values.
  • If multiplying by a decimal, count the total number of decimal places in both numbers you're multiplying.
  • Perform the multiplication as if they were whole numbers, then place the decimal point in the product accordingly.
For example, in the problem's first step: \( 840,000 \times 0.03 = 25,200 \). We treated 0.03 like a whole number during the multiplication, but then we arranged the decimal point based on the two decimal places from 0.03.
Division
Division is another fundamental arithmetic operation. It鈥檚 the process of finding how many times one number is contained within another. The exercise鈥檚 denominator calculation, involving \(\frac{25,200}{0.126}\), showcases division. Here are some helpful tips:
  • If dealing with decimals, you can simplify by making the divisor a whole number.
  • For example, move the decimal point in both the divisor and dividend the same number of places.
  • Perform the division as you would with whole numbers and adjust the decimal in the quotient.
In the exercise's third step, we made use of this: \(\frac{25,200}{0.126} = 200,000\). Multiplying both 25,200 and 0.126 by 1,000 transforms it into a simpler division: \(\frac{25,200}{0.126} = \frac{25,200 \times 1,000}{0.126 \times 1,000} = \frac{25,200}{126} = 200,000\). This simplification aids in a more straightforward calculation!
Standard Notation
Standard notation means expressing numbers in the way most people are used to seeing them. This means not using any scientific notation or other forms. Here鈥檚 how to ensure you鈥檙e using standard notation effectively:
  • Count from the first digit on the left to determine the place value positions.
  • Use commas to separate every three digits for easier readability.
  • Keep decimals in their correct places without converting to fractions or scientific notation.
In the exercise, the final answer is expressed in standard notation: 200,000. Always double-check that your answer doesn't include unnecessary decimal places or complex conversions. This ensures clarity and ease of understanding.

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