# Standard Form Algebra

## Deeply test your understanding of standard form (scientific notation) by involving a little algebra.

##### Menu  Standard FormLevel 1Level 2Level 3HelpMore Indices

This is level 3: mixed standard form questions. You will be awarded a trophy if you get at least 7 correct and you do this activity online. All answers should be given in standard form. To type indices or exponents use the up arrow key ^ then type the index. Use the button provided to insert a multiplication sign.

 1 Simplify$$\sqrt{16 \times 10^{2p}}$$ = 2 Simplify$$\sqrt{a^2 \times 10^{6}}$$ when $$1 \le a \lt 10$$ = 3 Simplify$$\sqrt{9a^2 \times 10^{2p+4q}}$$ when $$\frac13 \le a \lt \frac{10}{3}$$ = 4 Simplify$$\sqrt{a^4b^6 \times 10^{-6}}$$ when $$10 \le a^2b^3 \lt 100$$ = 5 Simplify$$(a \times 10^{3})^2$$ when $$\sqrt{10} \le a \lt 10$$ = 6 Simplify$$(a \times 10^{p})^q$$ when $$100 \le a^q \lt 1000$$ = 7 Simplify$$\frac{a \times 10^5 \times b \times 10^p}{b \times 10^q}$$where$$1 \le a \lt 10$$ = 8 Simplify$$\frac{a^2 \times 10^{2p} \times b^3 \times 10^{-3q}}{a^2b^2 \times 10^{5q+2p-8}}$$where$$1000 \le b \lt 10000$$ = 9 Simplify$$(a \times 10^3) + (10a \times 10^2)$$ where $$0.5 \le a \lt 5$$ =
Check

This is Standard Form Algebra level 3. You can also try:
Level 1 Level 2

The questions in this exercise have been adapted from an exercise created by Transum subscriber Chris Boardman.

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

## More Activities:

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry:

"Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils.
Thanks again"

Comment recorded on the 17 June 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull:

"Dear Transum,

I love you website I use it every maths lesson I have with every year group! I don't know were I would turn to with out you!"

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

#### Tower of Hanoi

Move the pieces of the tower from one place to another in the minimum number of moves. This puzzle was invented in 1883 but is still as captivating today as it was all those years ago.

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

Subscribe

## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

## Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

## Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

For Students:

For All:

Scan the QR code below to visit the online version of this activity.

https://www.Transum.org/go/?Num=908

## Description of Levels

Close

Standard Form - Begin here if you prefer your standard form to come without algebra.

Level 1 - Simplifying expressions in standard form

Level 2 - Multiplication and division of numbers in standard form

Level 3 - Mixed standard form questions

More Indices including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

## Standard Form

Standard form, also known as scientific notation, is a way of conveniently writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation.

## Examples

3.48 x 104

= 3.48 x 10 x 10 x 10 x 10

= 3.48 x 10000

= 34800

3.48 x 10-2

3.48 x 1100

= 3.48 ÷ 100

= 0.0348

Finally note that any number raised to the power zero is 1 so:

3.48 x 100

= 3.48 x 1

= 3.48

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

### Typing Mathematical Notation

These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.

Close