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Chapter 5: Problem 166

In the following exercises, simplify. $$35(0.2)+(0.9)^{2}$$

Short Answer

Expert verified
7.81

Step by step solution

01

- Simplify the multiplication

First, simplify the term involving the multiplication. Calculate the product of 35 and 0.2: \[35 \times 0.2 = 7\]
02

- Simplify the exponent

Next, simplify the term involving the exponent. Calculate the square of 0.9: \[(0.9)^{2} = 0.81\]
03

- Add the results together

Finally, add the results from Step 1 and Step 2 together: \[7 + 0.81 = 7.81\]

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Key Concepts

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

Multiplication
Multiplication is the process of adding a number to itself a certain number of times. In this exercise, we perform the multiplication of 35 and 0.2.

When multiplying, it helps to break the numbers down into simpler forms. For instance, you can think of 35 as 35 ones, and you can multiply each one by 0.2. This can be broken down as follows:

  • First, 35 multiplied by 0.2 can be written as 35 times 2 divided by 10, which is easier: \[ 35 \times 0.2 = 35 \times \frac {2}{10} \]
  • Rewrite it as: \[ \frac {35 \times 2}{10} = \frac{70}{10} = 7 \]

Hence, 35 times 0.2 equals 7. Breaking the process down into smaller steps can make it easier to understand the multiplication.
Exponents
Exponents are used to indicate how many times a number, known as the base, is multiplied by itself. In the exercise, we need to simplify the square of 0.9.

The exponent is 2, so we multiply 0.9 by itself. Here's how:
  • First, we write it as: \[ (0.9)^2 = 0.9 \times 0.9 \]
  • We can break it down into simpler multiplication: \[ 0.9 \times 0.9 = 0.81 \]

So, \[ (0.9)^2 = 0.81 \]
Practicing with small numbers and breaking down each step helps in understanding how exponents work.
Addition
Addition is the process of combining two or more numbers to get their total. In the last step of the exercise, we add the results obtained from the multiplication and exponentiation.

The exercise involves adding 7 (from the multiplication 35 times 0.2) and 0.81 (from 0.9 squared) together to get:
  • Write it as: \[ 7 + 0.81 \]
  • Perform the simple addition: \[ 7 + 0.81 = 7.81 \]

Addition can be straightforward, especially with small numbers. Combining steps to ensure accuracy is key in getting the correct total.

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