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Chapter 5: Problem 124

In the following exercises, multiply. $$(0.6)(0.7)$$

Short Answer

Expert verified
0.42

Step by step solution

01

Understand the problem

The exercise asks to multiply two decimal numbers: 0.6 and 0.7.
02

Multiply the numbers without the decimal point

First, multiply the numbers as if they were whole numbers. Multiply 6 by 7, which equals 42.
03

Count the decimal places

In the original numbers, 0.6 has one decimal place and 0.7 also has one decimal place. Combined, they have a total of 2 decimal places.
04

Place the decimal point in the product

Place the decimal point in the product so it has the same number of decimal places as the sum of the decimal places in the original numbers. Therefore, 42 needs to be written as 0.42.

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Key Concepts

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

decimal multiplication
When multiplying decimals, it can be helpful to follow a few simple steps. Start by ignoring the decimal points and treat the numbers as whole numbers. For example, if you are multiplying 0.6 by 0.7, pretend you are multiplying 6 by 7. So, 6 times 7 equals 42.
  • Multiplying without decimal points initially helps to simplify the multiplication process
  • Remember to bring back the decimals at the end

This technique makes it easier to handle and understand the multiplication of decimals.
place value
Place value is crucial when dealing with decimals. Each digit in a decimal number has a specific place value, depending on its position relative to the decimal point. In 0.6 and 0.7, both numbers have one digit to the right of the decimal point 鈥� the tenths place.
  • The more places you have after the decimal, the smaller the value of each digit
  • Add up all the decimal places from each number you are multiplying

When you have two numbers like 0.6 (one decimal place) and 0.7 (one decimal place), you combine their places. So, you will have two decimal places in the final product. Therefore, when we get 42 from multiplying 6 and 7, reintroduce the decimal points to make it 0.42, as 42 with two decimal places becomes 0.42.
basic arithmetic
Understanding basic arithmetic is the foundation of learning more complex math concepts, such as multiplication of decimals. It includes knowing how to multiply, add, subtract, and divide numbers.
  • Strong arithmetic skills make dealing with decimals easier
  • Practice these basics to build confidence

In the given example, 0.6 multiplied by 0.7, we first perform the basic multiplication of 6 times 7 to get 42. Next, we use our place value knowledge to place the decimal in the correct spot, resulting in 0.42. By mastering these fundamental arithmetic skills, you can accurately and efficiently solve decimal multiplication problems.

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