/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 5 Write each number in scientific ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 5

Write each number in scientific notation, rounding to three significant figures. $$4.9812$$

Short Answer

Expert verified
The number in scientific notation is \(4.98 \times 10^0\).

Step by step solution

01

Identify the Coefficient and Write in Scientific Notation

When writing a number in scientific notation, we need a coefficient that is greater than or equal to 1 and less than 10. For the number 4.9812, the coefficient is already 4.9812 because it fits our requirement.
02

Rounding to Three Significant Figures

We need to round our coefficient, 4.9812, to three significant figures. The first three significant figures are 4, 9, and 8. The fourth figure (1) does not affect the rounding as it is less than 5. Therefore, the rounded coefficient remains 4.98.
03

Write in Scientific Notation

Now that we have our rounded coefficient as 4.98, the number in scientific notation becomes \(4.98 \times 10^0\). This is because the original number 4.9812 does not require shifting the decimal point to convert to scientific notation.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Significant Figures
When working with numbers, significant figures are crucial in ensuring precision. Significant figures are the digits in a number that carry meaningful information about its precision. These include all non-zero digits, any zeros between non-zero digits, and sometimes trailing zeros when they are in a decimal.
  • Understanding significant figures helps us know the precision of measurements.
  • These figures determine the number of digits to maintain when rounding numbers.
  • In any computation, it's essential to use significant figures to preserve accuracy.
In our exercise, the number 4.9812 has four significant figures: 4, 9, 8, and 1. When converting this to three significant figures, we only keep the digits 4, 9, and 8; the digit after these three figures guides our rounding decision. This precision helps in conveying data accurately in scientific and technical fields.
Rounding Numbers
Rounding numbers makes them simpler while keeping their value close to what it was. This is often necessary to limit significant figures, enhance readability, or comply with specific conventions. The general rules for rounding are:
  • If the digit following your last significant figure is less than 5, you leave your number as is.
  • If the digit is 5 or greater, you round up the last significant figure by one.
In our exercise example, the number 4.9812 is rounded to three significant figures by examining the digit right after these figures. The digit '1' is less than 5, so the third significant digit '8' stays the same, resulting in 4.98. This step ensures the number stays precise enough for practical purposes but is easier to work with in scientific contexts.
Mathematical Notation
Mathematical notation allows complex ideas to be written simply and unambiguously. Scientific notation is a form of mathematical notation used to express very large or small numbers compactly.Scientific notation consists of:
  • A coefficient (between 1 and less than 10).
  • A power of ten.
In our example, 4.9812 is written in scientific notation as 4.98 since we don't need to move the decimal. Therefore, it becomes 4.98 \( \times 10^0 \). This approach helps to present numbers neatly, particularly in disciplines like science and engineering where precision needs to balance with conciseness.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Express the inequality, or inequalities, using absolute value. $$-6

Determine whether each statement is true for all real numbers \(x\). If the statement is false, then indicate one counterexample, i.e. a value of \(x\) for which the statement is false. $$x^{3}+1>x^{3}$$

Simplify the algebraic fraction. $$\frac{a-\frac{a^{2}}{b}}{\frac{a^{2}}{b}-a}$$

Express the inequality, or inequalities, using absolute value. $$x \leqslant-4 \text { or } x \geqslant 4$$

Evaluate each absolute value expression. $$|-3|-|-8|$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.