Call Now to Set Up Tutoring:

(888) 888-0446

HiSET: Math : Solve problems using scientific notation

Study concepts, example questions & explanations for HiSET: Math

Create An Account

All HiSET: Math Resources

125 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Solve Problems Using Scientific Notation

Simplify the following expression using scientific notation.

$(1.26\times10^6)+(2.4\times10^4)$

Possible Answers:

$1.284\times10^6$

$1.2624\times10^6$

$1.24677\times10^6$

$1.284\times10^5$

$1.5\times10^6$

Correct answer:

$1.284\times10^6$

Explanation:

You can solve this problem in several ways. One way is to convert each number out of scientific notation and write it out fully, then find the sum of the two values and convert the answer back into scientific notation.

$1.26\times10^6+2.4\times10^4 \newline = 1,260,000+24,000 \newline = 1,284,000 \newline = 1.284\times10^6$

Another, potentially faster, way to solve this problem is to convert one answer into the same scientific-notational terms as the other and then sum them.

$1.26\times10^6+2.4\times10^4$

$2.4\times10^{4}=0.024\times10^{6}$

$1.26\times10^6+0.024\times10^6=(1.26+0.024)\times10^6=1.284\times10^6$

Report an Error

Example Question #1 : Solve Problems Using Scientific Notation

Multiply, and express the product in scientific notation:

$7,200,000 \times 5,000,000$

Possible Answers:

$3.6 \times 10^{36}$

$3.6 \times 10^{13}$

$3.6 \times 10^{6}$

$3.6 \times 10^{12}$

$3.6 \times 10^{37}$

Correct answer:

$3.6 \times 10^{13}$

Explanation:

Convert 7,200,000 to scientific notation as follows:

Move the (implied) decimal point until it is immediately after the first nonzero digit (the 7). This required moving the point six units to the left:

$7,200,000. \Rightarrow 7.200000$

It follows that 7,200,000 can be rewritten as $7.2 \times 10^{6}$ .

By similar reasoning, 5,000,000 can be rewritten as $5 \times 10^{6}$ .

Thus,

$7,200,000 \times 5,000,000$

$= (7.2\times 10 ^{6} )\times (5 \times 10^{6} )$

Rearrange and regroup the expressions so that the powers of ten are together:

$= (7.2\times 5) \times (10 ^{6} \times 10^{6} )$

Multiply the numbers in front. Also, multiply the powers of ten by adding exponents:

$= 36 \times 10 ^{6+6}$

$= 36 \times 10 ^{12}$

In order for the number to be in scientific notation, the number in front must be between 1 and 10. An adjustment must be made by moving the implied decimal point in 36 one unit left. It follows that

$36 = 3.6 \times 10^{1}$

Therefore,

$36 \times 10 ^{12} = (3.6 \times 10^{1}) \times 10 ^{12}$

$= 3.6 \times 10^{1+12}$

$= 3.6 \times 10^{13}$ ,

the correct response.

Report an Error

Example Question #1 : Solve Problems Using Scientific Notation

Multiply:

$5,000,000 \times 120,000,000$

Express the product in scientific notation.

Possible Answers:

$60 \times 10^{14}$

$60 \times 10^{13}$

None of the other choices gives the correct response.

$6 \times 10^{13}$

$6 \times 10^{14}$

Correct answer:

$6 \times 10^{14}$

Explanation:

Scientific notation refers to a number expressed in the form

$\pm a \times 10^{N}$ ,

where $1 \le a < 10$ and is an integer.

Each factor can be rewritten in scientific notation as follows:

$5,000,000 = 5 \times 1,000,000 = 5 \times 10^{6}$

$120,000,000 = 1.2 \times 100,000,000 = 1.2 \times 10^{8}$

Now, substitute:

$5,000,000 \times 120,000,000$

$= 5 \times 10^{6} \times 1.2 \times 10^{8}$

$=( 5\times 1.2) \times (10^{6} \times 10^{8})$

$= 6 \times 10^{6} \times 10^{8}$

Apply the Product of Powers Property:

$= 6 \times 10^{6+8}$

$= 6 \times 10^{14}$

This is in scientific notation and is the correct choice.

Report an Error

View Tutors

Germaine
Certified Tutor

Princeton University, Bachelor in Arts, Philosophy.

View Tutors

Sakshi
Certified Tutor

M S Ramaiah College of Arts, Science and commerce, Bachelor, Chemistry, Biotechnology, Microbiology .

View Tutors

Tola
Certified Tutor

Indiana University-Bloomington, Bachelor in Arts, Chemistry. Harvard University, Doctor of Medicine, Homeopathic Medicine.

All HiSET: Math Resources

125 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

LSAT Tutors in Phoenix, Spanish Tutors in Dallas Fort Worth, SSAT Tutors in Los Angeles, English Tutors in Boston, GMAT Tutors in Seattle, Reading Tutors in Philadelphia, Chemistry Tutors in Chicago, Calculus Tutors in Washington DC, Statistics Tutors in Washington DC, GMAT Tutors in Philadelphia

Popular Courses & Classes

SAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Phoenix, Spanish Courses & Classes in Denver, Spanish Courses & Classes in Boston, GMAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Washington DC, ISEE Courses & Classes in Seattle, Spanish Courses & Classes in Houston, GRE Courses & Classes in Atlanta

Popular Test Prep

SSAT Test Prep in Seattle, GMAT Test Prep in Dallas Fort Worth, GRE Test Prep in Chicago, GMAT Test Prep in Los Angeles, LSAT Test Prep in Chicago, SAT Test Prep in Phoenix, LSAT Test Prep in New York City, LSAT Test Prep in Miami, SSAT Test Prep in Washington DC, LSAT Test Prep in Phoenix

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

HiSET: Math : Solve problems using scientific notation

Study concepts, example questions & explanations for HiSET: Math

All HiSET: Math Resources

Example Questions

Example Question #1 : Solve Problems Using Scientific Notation

Example Question #1 : Solve Problems Using Scientific Notation

Example Question #1 : Solve Problems Using Scientific Notation

All HiSET: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: