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Chapter 10: Problem 45

Use a calculator to find each product. Round to the nearest tenth. $$3.14 \cdot 4^{2}$$

Short Answer

Expert verified
50.2

Step by step solution

01

Calculate the exponent

First, calculate the exponent in the expression. We have \(4^2\), which means 4 multiplied by itself. Calculate: \[4^2 = 4 \times 4 = 16\].
02

Multiply by the constant

Now, you'll multiply the result from Step 1 by the constant 3.14. We have: \(3.14 \times 16\).
03

Use a calculator

Using a calculator, compute the product of 3.14 and 16. The result of this multiplication is \(50.24\).
04

Rounding to the nearest tenth

Finally, round the result to the nearest tenth. The number 50.24 rounds to 50.2 because the digit in the hundredths place is less than 5.

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Key Concepts

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

Understanding Exponents
Exponents are a way to represent repeated multiplication. Instead of writing a number multiplied by itself multiple times, we use an exponent to indicate this repetition.
For example, in the expression \(4^2\), the number 4 is called the base, and 2 is the exponent. When you see \(4^2\), it means you multiply the base, which is 4, by itself as many times as the exponent specifies.
  • Calculation: \(4^2 = 4 \times 4\)
  • Result: \(4^2 = 16\)
Exponents are helpful in compactly representing large computations and are common in both math and science.
Basics of Multiplication
Multiplication is one of the fundamental operations of arithmetic. It combines groups of equal sizes into a larger total. In our example, we are multiplying 3.14 by 16. This is part of Step 2 in the original solution.
  • Follow this process: Multiply 3.14 by 16 to find the total product.
  • Steps: Write 3.14 vertically over 16, and then multiply each digit in 3.14 by each digit in 16.
Multiplication helps us calculate totals efficiently, rather than adding repeatedly.
Using a Calculator Efficiently
Calculators are amazing tools that speed up mathematical processes and help us with accuracy in arithmetic operations like multiplication.
The primary step in using a calculator is understanding which keys to press:
  • Input the first number (e.g., 3.14)
  • Press the multiplication symbol (脳)
  • Input the second number (e.g., 16)
  • Press the equals sign (=) to get the result
Calculators are precise and can handle a wide variety of operations, but it's essential to know how to input commands correctly to obtain the right answer.
Understanding Rounding Numbers
Rounding numbers simplifies them while keeping them close to the original value. Rounding to the nearest tenth involves looking at the hundredths digit. For example, in the number 50.24:
  • The tenths digit is 2
  • The hundredths digit is 4
Since the hundredths digit is 4, which is less than 5, the tenths digit remains the same. Rounding follows this rule:
  • If the digit is 5 or more, increase the tenths by 1
  • If the digit is less than 5, the tenths digit stays the same
So, 50.24 rounds to 50.2.

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Most popular questions from this chapter

TRACK AND FIELD Heather needs to average 11.4 seconds in the 100 -meter dash in six races to qualify for the championship race. The mean of her first five races was 11.2 seconds. What is the greatest time that she can run and still qualify for the race?

How is the area of a parallelogram related to the area of a rectangle? Describe the similarities and differences between a rectangle and a parallelogram, and draw a diagram that shows how the area of a parallelogram is related to the area of a rectangle.

Use the following information. An equilateral figure is one in which all sides have the same measure. An equiangular figure is one in which all angles have the same measure. Is it possible for a quadrilateral to be equilateral without being equiangular? If so, explain with a drawing.

Solve equation. \(2 x+134=360\)

OPEN ENDED Draw two examples of composite figures. Describe how you would find the area of each figure.
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