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Chapter 7: Problem 14

Write the percent equation. Then solve for the unknown amount. What is \(0.4 \%\) of \(75 ?\)

Short Answer

Expert verified
0.3

Step by step solution

01

Understand the Percent Equation

The percent equation is given by the formula \[ \text{part} = \frac{\text{percent}}{100} \times \text{whole} \]. In this problem, the percent is 0.4%, and the whole is 75.
02

Substitute the Known Values

Substitute the percent and the whole into the percent equation: \[ \text{part} = \frac{0.4}{100} \times 75 \].
03

Calculate the Fraction

Calculate the fraction \[ \frac{0.4}{100} \]. This equals 0.004.
04

Multiply by the Whole

Multiply the result from Step 3 by 75: \[ 0.004 \times 75 = 0.3 \].

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Key Concepts

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

Percent Calculation
Percent calculations are a fundamental part of mathematics. In the context of our problem, we need to find what 0.4% of 75 is. A percent represents a part out of 100. Hence, 0.4% means 0.4 out of every 100 units. To solve this, we use the percent equation: \( \text{part} = \frac{\text{percent}}{100} \times \text{whole} \)
We substitute the values into this formula to find our answer. For our problem: \( \text{part} = \frac{0.4}{100} \times 75 \)
This means we first convert the percentage to a fraction or decimal and then multiply by the total amount.
Fractions
Understanding fractions is crucial for solving percent equations. A fraction represents a division of a whole into parts. In our problem, we divide 0.4 by 100 to convert the percent into a decimal: \( \frac{0.4}{100} = 0.004 \)
This step is essential because it simplifies our calculations and makes multiplication easier.
Fractions are useful in various mathematical contexts, so mastering them is beneficial. Make sure you understand how to convert between fractions, decimals, and percentages.
Multiplication
Multiplication is the final step in solving our percent equation. After converting 0.4% to 0.004, we multiply this result by the total amount(i.e., 75): \( 0.004 \times 75 = 0.3 \)
This operation is straightforward but requires precision. It's helpful to double-check your steps to avoid mistakes. When multiplying, keep track of the decimal places to ensure your answer is accurate. Multiplication is one of the basic operations you'll frequently use in math, so practicing it will help you become more proficient.
Now, you know that 0.4% of 75 is 0.3.

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Most popular questions from this chapter

Match the percent with its fraction form. a. \(\frac{3}{2}\) b. \(\frac{3}{4}\) c. \(\frac{2}{3}\) d. \(\frac{1}{10}\) e. \(\frac{9}{10}\) f. \(\frac{1}{4}\). $$150 \%$$

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{13}{15}$$

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Find the total amount in an account for an investment subject to the following conditions. Principal $$\$ 10,000$$ Annual Interest Rate $$6 \%$$ Time, Years $$1 \frac{1}{2}$$ Compounded Quarterly Total Amount __________

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