1.2.6. Scientific Notation

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Name	Status	Author	Last Modified
1.2.6. Scientific Notation	Ready to use	Merryn Horrocks	28/06/2023 05:35
1.2.6 Task: Write numbers in scientific notation	Ready to use	Merryn Horrocks	08/07/2023 07:45

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Question statement

Scientific Notation

It is often necessary to use very large or very small numbers such as $78000000$ and $0.00000034$ .
Scientific notation can be used to express such numbers in a more concise form. Each number is written in the form

$a \times 10^n$

where $a$ is a number between $1$ and $10$ . We can make use of the following facts:

$10 = 10^1$ ; $\quad 100 = 10^2$ ; $\quad 1000 = 10^3\quad$ and so on

and

$0.1 = 10^{-1}$ ; $\quad 0.01 = 10^{-2}$ ; $\quad 0.001 = 10^{-3}\quad$ and so on.

For example,

the number $5000$ can be written $5 \times 1000 = 5 \times 10^3$
the number $403$ can be written $4.03 \times 100 = 4.03 \times 10^2$
the number $0.009$ can be written $9 \times 0.001 = 9 \times 10^{-3}$

Furthermore, to multiply a number by $10^n$ the decimal point is moved $n$ places to the right if $n$ is a positive integer, and $n$ places to the left if $n$ is a negative integer. (If necessary additional zeros are inserted to make up the required number of digits before the decimal point.)

Give any introductory information the student needs.

			Name	Type	Generated Value

q1base	decimal	dec("9.8554")
q1idx	integer	-5
q1expr	decimal	dec("0.000098554")
q2b1	decimal	dec("8.9")
q2b2	decimal	dec("5.3")
q2i1	integer	23
q2i2	integer	-36
q2expr	expression	8.910^235.3*10^(-36)
q2base	number	4.717
q2idx	integer	-12
q2ans	string	4.717e-12

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
decimal(random(10001..99999)/10000)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `decimal`

dec("9.8554")

→ Used by:

q1expr

This variable doesn't seem to be used anywhere.

Parts

Task 1 Gap-fill
1. Gap q1Base Number entry
  Add
2. Gap q1Idx Number entry
  Add
Information only

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Write $\var{q1Expr}$ in scientific notation:

q1Base $\times 10$ ^q1Idx

Advice

Give a worked solution to the whole question.

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There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Information only

This question is used in the following exam:

HELM Book 1.2 Indices by Merryn Horrocks in HELM books.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Merryn Horrocks 1 year, 9 months ago

Merryn Horrocks 2 years, 10 months ago

Merryn Horrocks 2 years, 10 months ago

Scientific Notation

Error in variable testing condition

Error

Warning

Generated value: `decimal`

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Gap-fill

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1.2.6. Scientific Notation

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Merryn Horrocks 1 year, 9 months ago

Merryn Horrocks 2 years, 10 months ago

Merryn Horrocks 2 years, 10 months ago

Scientific Notation

Error in variable testing condition

Error

Warning

Generated value: decimal

Parts

Gap-fill

Generated value: `decimal`