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Chapter 2: Problem 14

Multiply as indicated. 14\. \(0.45 \times 100\)

Short Answer

Expert verified
45

Step by step solution

01

Understand the problem

Identify the numbers that need to be multiplied. Here, you are given the numbers 0.45 and 100.
02

Multiply the decimal by 100

To multiply a decimal by 100, move the decimal point two places to the right. So, moving the decimal point in 0.45 two places to the right gives 45.
03

Write the final answer

After moving the decimal point, the result is 45. Therefore, 0.45 multiplied by 100 equals 45.

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Key Concepts

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

decimal point
The decimal point is a dot used to separate the whole part of a number from its fractional part. In the example, the number 0.45 has a decimal point that separates 0 (the whole part) from 45 (the fractional part). Moving the decimal point is crucial when multiplying or dividing by powers of 10.

When you multiply by 10, 100, or 1000, the decimal point moves to the right. The number of places it moves depends on the zeros in the multiplier:
  • Multiplying by 10 moves the decimal one place to the right.
  • Multiplying by 100 moves the decimal two places to the right.
  • Multiplying by 1000 moves the decimal three places to the right.
Understanding how the position of the decimal point changes can help you solve decimal multiplication problems easily.
multiplication
Multiplication is one of the basic arithmetic operations. It combines two quantities into a single product. When multiplying decimals, follow these simplified steps:
  • Ignore the decimal points and multiply the numbers as if they are whole numbers.
  • Count the total number of decimal places in the factors.
  • Place the decimal point in the product so that it has the same number of decimal places as the total counted in the previous step.
In our example, multiplying 0.45 by 100 means you move the decimal point in 0.45 two places to the right, resulting in 45.

Practicing these steps helps build a strong foundation in decimal multiplication and ensures accurate results.
place value
Place value refers to the value of each digit in a number based on its position. Understanding place value is essential in working with decimals and performing operations accurately.

Consider the number 0.45:
  • The digit 4 is in the tenths place, meaning it represents 4 tenths or 0.4.
  • The digit 5 is in the hundredths place, meaning it represents 5 hundredths or 0.05.
When we multiply 0.45 by 100, we shift the decimal point two places to the right, changing the place values:
  • The 4 moves from the tenths place to the tens place, becoming 40.
  • The 5 moves from the hundredths place to the units place, becoming 5.
Thus, the result is 45, combining the place values of tens and units.

Grasping place value concepts ensures that you can correctly interpret and manipulate decimal numbers.

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Most popular questions from this chapter

Graph the solution set, and write it using interval notation \(-6 \leq \frac{1}{3} x+3 \leq 5\)

Graph the solution set, and write it using interval notation \(6 \leq 3(x-1)<18\)

Solve each problem. In each case, give an equation using \(x\) as the variable and give the answer. See Examples 1 and \(2 .\) The sum of a number and 9 is \(-26 .\) What is the number?

If 2 is added to five times a number, the result is equal to 5 more than four times the number. Find the number.

If 4 is added to twice a number and this sum is multiplied by \(2,\) the result is the same as if the number is multiplied by 3 and 4 is added to the product. What is the number?
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