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Chapter 7: Problem 13

Convert each number into scientific notation. $$90$$

Short Answer

Expert verified
90 = 9.0 脳 10鹿

Step by step solution

01

Identify the Coefficient

Scientific notation represents numbers as the product of a coefficient and a power of 10. The coefficient should be a number between 1 and 10. Identify the significant digits of the number 90.
02

Move the Decimal Point

To create the coefficient, move the decimal point in 90 to the right of the 9, making it 9.0.
03

Determine the Exponent

Count the number of places you moved the decimal point. There is 1 place from 90 to 9.0, so the exponent of 10 is 1.
04

Construct the Scientific Notation

Combine the coefficient and the power of 10 to convert the number into scientific notation: 90 = 9.0 脳 10鹿.

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Key Concepts

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

Coefficient
In scientific notation, the coefficient is a crucial part. It represents a value between 1 and 10.
For the number 90, we focus on the significant digit, which is 9.0 after moving the decimal point. This value comes from identifying the most significant digits while ensuring the coefficient stays between 1 and 10.
  • It removes insignificant trailing zeros.
  • Simplifies large or small numbers.
For instance, moving the decimal from 90 to 9.0 makes it easy to handle and read. This single, clear value (between 1 and 10) helps standardize numbers in scientific notation.
Decimal Point
Understanding the role of the decimal point is essential in scientific notation. For the number 90, you start with an assumed decimal point after the 0 (90 can be written as 90.0).
Moving this decimal point correctly determines the coefficient.
  • You place the decimal behind the first significant digit.
  • For 90, move it one place left to get 9.0.
This simplifies the number while preserving its value. It ensures numbers are in a manageable format, making calculations and comparisons easier.
Exponent
The exponent in scientific notation shows how many places the decimal point has been moved. For 90 converted to 9.0, the decimal point moved one place to the left.
The exponent becomes 1, denoted as 10鹿.
  • Positive exponent means move decimal point to the right to revert to original number.
  • Negative exponent means move decimal point to the left to revert to original number.
Combining the exponent with the coefficient (9.0 脳 10鹿) gives the scientific notation. This helps in tackling extremely large or tiny values efficiently.

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Most popular questions from this chapter

Simplify each of the following as completely as possible. $$\left(-x^{3} y\right)^{3}$$

Do your computation using scientific notation. $$\frac{0.003}{6000}$$

What can you say about the sign of the exponent of 10 of a number written in scientific notation if the number is bigger than \(1 ?\) If the number is smaller than \(1 ?\) Why?

Multiply out \((x+6)(x+4)\) and \((x-6)(x-4) .\) What is the effect of switching both \(+\) signs to \(-\) signs?

Convert each number into scientific notation. $$56 \times 10^{-2}$$
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