Problem 77
Question
Write each number in scientific notation. $$ 0.027 $$
Step-by-Step Solution
Verified Answer
The number \(0.027\) in scientific notation is \(2.7 \times 10^{-2}\).
1Step 1: Identify Your Base Number
First, look to get a number between 1 and 10 by shifting the decimal point. So, \(0.027\) becomes \(2.7\).
2Step 2: Count the Number of Decimal Places Moved
Since we moved the decimal two places to the right, the number is \(2.7\).
3Step 3: Write in Scientific Notation
Write the number as \(2.7\) times \(10^{-2}\) because the decimal was moved 2 places to the right to get the base number, hence the use of negative power.
Key Concepts
Decimal NumbersExponentsMathematical Notation
Decimal Numbers
Decimal numbers are a crucial part of everyday mathematics. They are a way to express numbers that are not whole and include fractions of whole numbers. A decimal number consists of a whole number part, a decimal point, and a fractional part. For instance, in the number \(0.027\), the whole number part is \(0\) and the fractional part is \(.027\).
Decimals make it easier to deal with fractions by representing them in a consistent and streamlined form. When managing large or small numbers, especially in scientific calculations, converting decimals to scientific notation can simplify the process. This is done by shifting the decimal point to express the number as a value between \(1\) and \(10\). For \(0.027\), this becomes \(2.7\) as the base number.
Understanding decimals helps in everyday applications like measuring, money transactions, and converting between different units. They are the basis for more complex mathematical operations like percentage, exponentials, and scientific notation.
Decimals make it easier to deal with fractions by representing them in a consistent and streamlined form. When managing large or small numbers, especially in scientific calculations, converting decimals to scientific notation can simplify the process. This is done by shifting the decimal point to express the number as a value between \(1\) and \(10\). For \(0.027\), this becomes \(2.7\) as the base number.
Understanding decimals helps in everyday applications like measuring, money transactions, and converting between different units. They are the basis for more complex mathematical operations like percentage, exponentials, and scientific notation.
Exponents
Exponents are a powerful mathematical notation used to represent repeated multiplication of the same number. When you have a number like \(10^2\), it means \(10\) multiplied by itself \(2\) times, resulting in \(100\).
Exponents are especially useful when expressing very large or small numbers in scientific fields. They serve as a concise way of capturing immense values or minuscule quantities. In scientific notation, exponents come into play to indicate how many places the decimal point has been moved. For example, in \(2.7 \times 10^{-2}\), the exponent \(-2\) shows that the original number \(0.027\) was adjusted by moving the decimal two places to the right.
Learning about exponents helps enhance your understanding of mathematics, as they appear in areas like algebra, calculus, and even in the understanding of scientific data. Mastery of exponents gives you the tools to solve equations more efficiently and interpret data in scales that might otherwise be difficult to conceptualize.
Exponents are especially useful when expressing very large or small numbers in scientific fields. They serve as a concise way of capturing immense values or minuscule quantities. In scientific notation, exponents come into play to indicate how many places the decimal point has been moved. For example, in \(2.7 \times 10^{-2}\), the exponent \(-2\) shows that the original number \(0.027\) was adjusted by moving the decimal two places to the right.
Learning about exponents helps enhance your understanding of mathematics, as they appear in areas like algebra, calculus, and even in the understanding of scientific data. Mastery of exponents gives you the tools to solve equations more efficiently and interpret data in scales that might otherwise be difficult to conceptualize.
Mathematical Notation
Mathematical notation is the language of mathematics, using symbols and signs to represent numbers, operations, and relationships between quantities. It includes numerals for numbers, operators for mathematical actions like addition, subtraction, and multiplication, and more specific symbols for advanced concepts.
The notation simplifies the way math is communicated and understood across different fields. In scientific notation, mathematical notation shows how numbers can be expressed in a form that simplifies calculations. For instance, the expression \(2.7 \times 10^{-2}\) uses symbols to efficiently convey that \(2.7\) is multiplied by \(10\) to the power of \(-2\), representing the number \(0.027\).
Mastering mathematical notation is vital as it equips you to decode complex equations and facilitate smooth communication of ideas in mathematics and science. It enhances your logical thinking and problem-solving skills, which are critical in academic and professional pursuits.
The notation simplifies the way math is communicated and understood across different fields. In scientific notation, mathematical notation shows how numbers can be expressed in a form that simplifies calculations. For instance, the expression \(2.7 \times 10^{-2}\) uses symbols to efficiently convey that \(2.7\) is multiplied by \(10\) to the power of \(-2\), representing the number \(0.027\).
Mastering mathematical notation is vital as it equips you to decode complex equations and facilitate smooth communication of ideas in mathematics and science. It enhances your logical thinking and problem-solving skills, which are critical in academic and professional pursuits.
Other exercises in this chapter
Problem 77
Explain how to find the least common denominator for denominators of \(x^{2}-100\) and \(x^{2}-20 x+100\).
View solution Problem 77
In Exercises \(57-84\), factor completely, or state that the polynomial is prime. $$x^{2}-12 x+36-49 y^{2}$$
View solution Problem 77
Give an example of two things that you do that are not commutative.
View solution Problem 78
Find each product. $$(x-y)\left(x^{2}+x y+y^{2}\right)$$
View solution