/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 47 Multiply. $$ 1000 \times 45.... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 47

Multiply. $$ 1000 \times 45.678 $$

Short Answer

Expert verified
The product is 45678.

Step by step solution

01

Understand the problem

The problem requires multiplying two numbers: 1000 and 45.678. The goal is to find the product of these numbers.
02

Set up the multiplication

Write the multiplication expression: \[1000 \times 45.678\]
03

Perform the multiplication

Multiply the two numbers directly. \[1000 \times 45.678 = 45678\]
04

Verify the result

Double-check the multiplication to ensure accuracy. The multiplication was performed correctly in step 3.

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Key Concepts

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

Basic Mathematics
Understanding basic mathematics is essential for solving problems involving decimal multiplication. The foundational concepts include addition, subtraction, multiplication, and division. In decimal multiplication, we also use the concept of place value. Decimals are numbers that have a whole number part and a fractional part, separated by a decimal point. Each digit after the decimal point represents a fraction of ten, like tenths, hundredths, thousandths, and so on. This knowledge helps us understand how to align and multiply decimal numbers accurately.
Decimal Multiplication
Decimal multiplication might sound tricky, but it's straightforward once you know the steps. Here's how to approach it:
  • Ignore the decimal points and multiply the numbers as whole numbers.
  • Count the total number of decimal places in both of the original numbers.
  • Place the decimal point in the product so that it has the same number of decimal places as the total count from the previous step.
In the given exercise, 1000 is a whole number with no decimal places, and 45.678 has three decimal places. Hence, the final product should have three decimal places, but since 1000 is a multiple of ten, directly multiplying simplifies the process and shifts the decimal three places to the right. This results in 45.678 becoming 45678.
Step-by-Step Problem Solving
Breaking down problems with a step-by-step approach makes them more manageable. Here鈥檚 how to solve the exercise problem step-by-step:
  • Step 1: Understand the problem.
    The task is to multiply 1000 by 45.678.
  • Step 2: Set up the multiplication.
    Write the numbers as you would for any multiplication.
  • Step 3: Perform the multiplication.
    Multiply the numbers while ignoring the decimals: When multiplying 1000 by 45.678 directly, we simplify as if multiplying whole numbers but consider the decimal place in the final product. This yields 45678.
  • Step 4: Verify the result.
    Double-check your multiplication to ensure accuracy. Confirm that the decimal places align correctly in the product.

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Most popular questions from this chapter

McDonald's Stock. Recently, McDonald's stock sold for \(\$ 158.81\) per share. Estimate how many shares could be purchased for \(\$ 4800\).

Add. $$ \begin{array}{r} 13.72 \\ 9.112 \\ 6542.7908 \\ +\quad 23.901 \\ \hline \end{array} $$

Daniel worked 53 hr during one week last summer. He earned \(\$ 13.50\) per hour for the first \(40 \mathrm{hr}\) and \(\$ 15.25\) per hour for overtime (hours exceeding 40 ). How much did Daniel earn during the week?

Find decimal notation for \(\frac{1}{9}, \frac{1}{99},\) and \(\frac{1}{999} .\) Observe the pattern and guess the decimal notation for \(\frac{1}{9999}\).

Subtract. $$ 34.07-30.7 $$
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