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Chapter 1: Problem 33

Write each number in decimal form. \(1.4 \times 10^{0}\)

Short Answer

Expert verified
In decimal form, the number is 1.4.

Step by step solution

01

Identify the Base Number

The given expression is \(1.4 \times 10^{0}\). The base number here is 1.4, which is the number we begin with.
02

Understand the Power of Ten

Next, we look at the exponent, which is \(0\). Recall that any number raised to the power of 0 is equal to 1. So, \(10^{0} = 1\).
03

Multiply the Base and Power of Ten

Now, multiply the base number by the result of the power of ten: \(1.4 \times 1 = 1.4\). This multiplication allows us to express the number in decimal form.

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Key Concepts

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

Decimal Form
Decimal form is a way of writing numbers that shows all the digits before and after a decimal point. It's a standard format that makes it easy to understand and compare numbers.
  • In this context, the decimal form allows us to avoid using powers of ten notation, presenting numbers in a straightforward manner.
  • When you convert a number from scientific notation into decimal form, you're essentially writing it out completely, with all the digits visible.
It's like writing out a complete sentence instead of using abbreviations. For example, the expression \(1.4 \times 10^{0}\) simplifies to 1.4 in decimal form. Here, you don't need any extra zeros, just as you would omit unnecessary abbreviations in a sentence.
Powers of Ten
Powers of ten are a fundamental concept in mathematics, often used to express very large or very small numbers in a compact form. This notation uses the base number 10 raised to an exponent.
  • The exponent tells us how many times 10 is multiplied by itself. For instance, \(10^{2}\) means 10 is multiplied by itself twice: \(10 \times 10 = 100\).
  • When the exponent is positive, it indicates a large number, and when it's negative, it represents a small number.
  • Certain powers, like \(10^{0}\), have special rules. Any number to the power of zero equals 1, regardless of the base number.
Understanding these rules helps you convert numbers from scientific notation to decimal form effortlessly, as seen in the example \(10^{0} = 1\).
Multiplication
Multiplication is one of the basic arithmetic operations used to combine numbers. It can simplify how we represent and calculate numbers, particularly within scientific notation.
  • When multiplying a number by 1, the original number remains unchanged. This principle applies to the expression \(1.4 \times 10^{0}\), where the multiplication results in 1.4 because \(10^{0} = 1\).
  • This operation is crucial in scientific notation because it's used to adjust the base number according to the power of ten.
  • The process makes it easier to switch between scientific notation and decimal form while maintaining the number's actual value.
By practicing multiplication and understanding its effects, you can transition smoothly between different numeric forms, contributing to a more comprehensive understanding of numbers.

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Most popular questions from this chapter

Determine the precision of each measurement. \(3.00 \times 10^{-4} \mathrm{~kg}\)

Determine the precision of each measurement. \(4 \overline{0} 00 \mathrm{~N}\)

Use the rules for addition of measurements to add each set of measurements. $$ 36.8 \mathrm{~m} ; 147.5 \mathrm{~cm} ; 1.967 \mathrm{~m} ; 125.0 \mathrm{~m} ; 98.3 \mathrm{~cm} $$

Determine the precision of each measurement. \(70.00 \mathrm{~m}^{2}\)

Determine the precision of each measurement. \(2.4 \times 10^{3} \mathrm{~kg}\)
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