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Chapter 7: Problem 16

Multiply. $$36.5 \cdot \frac{1}{1,000} \cdot 100$$

Short Answer

Expert verified
3.65

Step by step solution

01

Simplify the Fraction

First, solve the fraction \( \frac{1}{1,000} \). This fraction represents 0.001 in decimal form. So, \( \frac{1}{1,000} = 0.001 \).
02

Multiply with the Decimal

Next, multiply 36.5 by the decimal equivalent of the fraction obtained in Step 1.\[ 36.5 imes 0.001 = 0.0365 \]
03

Multiply by 100

Finally, use the result from Step 2 and multiply it by 100.\[ 0.0365 imes 100 = 3.65 \]

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Key Concepts

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

Fractions and Decimals
In mathematics, fractions and decimals are just two ways of representing the same kinds of numbers - those that aren't whole.
  • A fraction like \( \frac{1}{1,000} \), tells us directly how many parts, out of a whole, we have.
  • This fraction, for example, means one part of a thousand, and it is the same as writing 0.001 in decimal form.
  • Decimals make it easy to perform calculations especially when dealing with powers of ten like 10, 100, 1,000, and so on.
Converting fractions to decimals makes multiplication straightforward as decimals align with our base-ten number system. So, next time you see a fraction like \( \frac{1}{1,000} \), think of how it translates to a neat little decimal point - 0.001.
Basic Arithmetic Operations
Arithmetic operations such as addition, subtraction, multiplication, and division are the building blocks of mathematics. Here, we'll focus on multiplication, a fundamental operation.
  • Multiplication is repeated addition. For instance, multiplying 36.5 by 0.001 means we are adding 36.5, a very tiny amount of 0.001 times.
  • To make it easy, align the decimal points when multiplying by small decimal or fractional values as it helps maintain precision.
Understanding the underlying arithmetic operation helps with conceptual clarity. By grasping these operations deeply, you will become more equipped to tackle more complex computations with ease.
Mathematical Problem-Solving
Mathematical problem-solving is about figuring out the best path to arrive at a solution.
  • Start by identifying what the problem demands: here, it's multiplying a decimal by a fraction, and then by 100.
  • Breaking down the problem into simple, manageable steps like converting fractions to decimals can significantly simplify the process.
  • Each multiplication step builds on the previous result, illustrating the power of orderly computation.
Strong problem-solving skills arise from practice and familiarity with different types of numbers and operations. The goal is to approach each problem methodically and with confidence, ensuring accuracy and efficiency in calculations.

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Most popular questions from this chapter

Write as a percent. Write the remainder in fractional form. $$2 \frac{5}{8}$$

Write as a percent. $$0.62$$

The problems below will allow you to review subtraction of fractions and mixed numbers. $$\frac{7}{10}-\frac{1}{5}$$

Write as a percent. Write the remainder in fractional form. $$\frac{7}{30}$$

Multiply. $$0.15(63)$$
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