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Chapter 7: Problem 3

Convert each number into scientific notation. $$0.0453$$

Short Answer

Expert verified
4.53 x 10^{-2}.

Step by step solution

01

Understand the Problem

The task is to convert the number 0.0453 to scientific notation.
02

Identify the Significant Figures

Locate the significant figures in the number. For 0.0453, the significant figures are 4, 5, and 3.
03

Move the Decimal Point

Move the decimal point to the right of the first significant figure. In 0.0453, this means moving the decimal point so it comes after the 4, resulting in 4.53.
04

Count the Decimal Movements

Count the number of places the decimal point was moved. For 0.0453, the decimal was moved 2 places to the right.
05

Write in Scientific Notation

Combine the coefficient (the number with the decimal adjusted) with the power of 10. Since the decimal was moved 2 places, the exponent will be -2. Therefore, 0.0453 in scientific notation is written as 4.53 x 10^{-2}.

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Key Concepts

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

Concept of Significant Figures
Significant figures represent the crucial digits in a number. They hint at the precision of a measurement or calculation. In the number 0.0453, the significant figures are 4, 5, and 3.
Why are these significant?
Because they carry meaningful information about the precision of the measurement.
Here鈥檚 how you identify significant figures:
  • All non-zero digits are significant.
  • Any zeros between significant digits are also significant.
  • Leading zeros are not significant - they only serve as placeholders.
By recognizing these, you鈥檒l know which numbers to keep when converting into scientific notation.
Understanding the Decimal Point
The decimal point is a dot used to separate the whole number part from the fractional part of a number. In scientific notation, understanding and correctly moving the decimal point is crucial.
Let鈥檚 look at the same example: 0.0453.
To convert a number to scientific notation, you must move the decimal point next to the first significant figure.
In 0.0453, move the decimal point 2 places to the right, placing it after 4 to get 4.53
So, you get a number (between 1 and 10) multiplied by a power of 10.
Role of Exponents in Scientific Notation
Exponents are used in scientific notation to show how many times you multiply or divide the number by 10. Specifically, for numbers less than 1 (like 0.0453), use a negative exponent.
After moving the decimal point, count the number of places it was moved.
Here, from 0.0453 to 4.53, moved 2 places to the right. Therefore, this becomes an exponent of -2.
So, 0.0453 becomes 4.53 x 10^{-2} in scientific notation.
Always remember:
  • Positive exponents indicate large numbers.
  • Negative exponents indicate small numbers (less than 1).

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Most popular questions from this chapter

Multiply out each of the following. As you work out the problems, identify those exercises that are either a perfect square or the difference of two squares. $$(2 y-5)(4 y+3)$$

Estimate the answer without actually carrying out the computation and make the most appropriate choice. If you multiply \(7,250\) by \(0.004,\) the result is closest to (a) 0.3 (b) 3 (c) 30 (d) 300 (e) 3000

perform the indicated operation and simplify. $$\text { Solve for } x: \frac{x}{3}-\frac{x}{4}=3$$

Do your computation using scientific notation. $$(0.004)(250)$$

Multiply out each of the following. As you work out the problems, identify those exercises that are either a perfect square or the difference of two squares. $$\left(x^{3}+y^{2}\right)^{2}$$
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