/*! 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 47 Convert to standard notation. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 47

Convert to standard notation. $$ 4.03 \text { trillion } $$

Short Answer

Expert verified
4.03 trillion is 4,030,000,000,000 in standard notation.

Step by step solution

01

Understand the term 'trillion'

In standard notation, 'trillion' refers to a value of 10 to the 12th power. In other words, 1 trillion is represented as 1,000,000,000,000.
02

Convert Trillion to Standard Notation

Take the given number 4.03 and multiply it by the standard value of a trillion. This means performing the multiplication: \( 4.03 \times 10^{12} \).
03

Write the result in standard notation

Carry out the multiplication: \( 4.03 \times 10^{12} = 4,030,000,000,000 \).

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.

trillion conversion
To understand 'trillion conversion', you first need to know what 'trillion' means. In mathematics, a trillion is represented as the number 1 followed by 12 zeros. This makes 1 trillion equal to 1,000,000,000,000. So, if you are asked to convert a number like 4.03 trillion into standard notation, you will first need to recognize that you need to multiply by 10 to the 12th power (\((10^{12})\)). Starting with 4.03, you multiply as follows: $$4.03 \times 10^{12} = 4,030,000,000,000.$$ This process is known as 'trillion conversion' and allows you to convert large numbers that are expressed in trillions into standard notation.
scientific notation
Scientific notation is a way to express very large or very small numbers in a more compact form. It uses the power of ten to simplify the number. For instance, instead of writing out 4,030,000,000,000, you can express it as $$4.03 \times 10^{12}.$$ Here's how it works:
  • Identify the significant digits. This is usually a number between 1 and 10.
  • Count how many places you move the decimal point to get from the original number to the significant digits.
  • Express the number as the significant digits multiplied by 10 raised to the power of the number of places you moved the decimal point.
Using the above example, 4,030,000,000,000 in scientific notation becomes 4.03 (the significant digits) multiplied by $$10^{12}$$. Scientific notation is especially useful in fields like physics and engineering, where you deal with either very large or very small measurements.
mathematical operations
Mathematical operations involving large numbers, such as those in the trillions, can often be simplified using scientific notation. When performing operations like addition, subtraction, multiplication, or division, scientific notation makes the calculations more manageable. Suppose you need to multiply a number in scientific notation. For example, multiplying $$4.03 \times 10^{12}$$ by $$2 \times 10^{3}$$:
  • Multiply the significant digits: $$4.03 \times 2 = 8.06$$.
  • Add the exponents of 10: $$10^{12} \times 10^{3} = 10^{15}$$.
  • Combine these results: $$8.06 \times 10^{15}$$.
Here's another example involving addition: Adding $$3.2 \times 10^{12}$$ to $$4.03 \times 10^{12}$$:
  • Keep the exponent the same: $$10^{12}$$.
  • Add the significant digits: $$3.2 + 4.03 = 7.23$$.
  • Combine these results: $$7.23 \times 10^{12}$$.
By using scientific notation, the process of performing mathematical operations becomes clearer and easier to handle, especially for students dealing with very large numbers.

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

Solve. A family invests \(\$ 4000\) in an account paying \(6 \%\), compounded monthly. How much is in the account after 5 months?

In baseball, the strike zone is normally a 17 -in. by 30 -in. rectangle. Some batters give the pitcher an advantage by swinging at pitches thrown out of the strike zone. By what percent is the area of the strike zone increased if a 2 -in. border is added to the outside?

Solve. The sales tax on the purchase of a used car is \(\$ 434\) and the sales tax rate is \(7 \%\). What is the purchase price?

A car generally depreciates \(25 \%\) of its original value in the first year. A car is worth \(\$ 27,300\) after the first year. What was its original cost?

Solve. California Sales Tax. The sales tax rate in California is \(7.25 \%\). How much sales tax is charged on a purchase of 4 contour foam travel pillows at \(\$ 39.95\) each? What is the total price?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Decision 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.