Vous êtes sur la page 1sur 5

# Topic 5: Operations with numbers in scientific notation

Multiplying
When multiplying numbers in scientific notation, the number part is multiplied and the
exponent part is multiplied using exponent rules.
Example

3.1 10 1.4 10
3.1 1.4 10 10
2

4.34 106
4.34 104

rearrange

It is important to look at the solution to see if the answer is still in scientific notation.

In the example below, an adjustment is required to put the answer into scientific
notation.

5.2 10 3.5 10
5.2 3.5 10 10
5

rearrange

18.2 105 9
18.2 1014 The number 18.2 is not in the range 1 to 9.9999,
1.82 101 1014 18.2 1.82 101

1.82 101 14
1.82 1013
The speed of light is approximately 3 10 m/sec. How far
will it travel in 5 hours?
8

5 hours
= 5 60 minutes
= 5 60 60 seconds
=18000 seconds
=1.8 104seconds
Distance covered speedtime
3 108 1.8 104
5.5 1012 metres

Version 1

## Exponents & Scientific Notation

01/07/2010

Dividing
Dividing numbers in scientific notation is similar to multiplication. The number part is
divided as usual and the exponent part is divided using exponent rules.
Example:

6.25 107
5.1 102
(6.25 5.1) (107 102 )

1.2255 107 2
1.2255 109
As in multiplying, it is important to look at the solution to see if the answer is still in
scientific notation.
In the example below, an adjustment is required to put the answer into scientific
notation.

3.12 107
7.36 104
(3.12 7.36) (107 104 )
0.4239 1074
0.4239 1011 The number 0.4239 is not in the range 1 to 9.9999,
4.239 101 1011 0.4239=4.239 101
4.239 1012
24

## The mass of a hydrogen atom is 1.6 10 grams. How

3
many atoms are there in 1 mg (10 gram) of hydrogen?

1 103
Number of atoms =
1.6 1024
(1 1.6) (103 1024 )

0.625 103 24
0.625 1021
6.25 101 1021
6.25 1020

Version 1

## Exponents & Scientific Notation

01/07/2010

When adding or subtracting any numbers, it is important that numbers of the same
place value are added or subtracted. When adding or subtracting whole numbers or
decimals these means lining up the numbers in place value rows.
With numbers written in scientific notation, lining up numbers in place values is
achieved by having exponent parts the same.
One exponent must be changed to be
the same as the other exponent.
Choosing the higher exponent makes
the finding then solution slightly
easier.

Add (3 10 ) and (4 10 )
5

(3 105 ) + (4 107 )
3 102 107 4 107
0.03 107 4 107 Both numbers are in the same place value
4.03 107

4

3
9

## 1.95 103 4.3 104

1.95 101 104 4.3 104
0.195 103 4.3 10 4
0.195 4.3 104
4.105 104

## 3.652 104 4.2 107

3.652 104 4.2 103 104
3.652 104 0.0042 104
(3.652 0.0042) 104
3.6562 104

Version 1

2 10 10

4. 3 0 0
0.1 9 5
4 .1 0 5
The largest number is negative
4 .1 0 5

Remember 4 is
larger than 7 .

## Exponents & Scientific Notation

01/07/2010

Calculator use:
To use scientific notation on your calculator, some calculators have a key marked
Exp , others EE .

## 4.25 106 is entered by the sequence 4.25 Exp Y6

8.75 1015 is entered by the sequence Y 8.75 Exp 15
1.6 1019 is entered by the sequence Y 1.6 Exp Y19
Using your calculator to change between scientific notation and standard notation
can be quite difficult. If you require this you will need to obtain the instructions for
your calculator and find out how to achieve this.
Performing an operation such as 2 1011 4.25 106 is entered as:
2 Exp 11[4.25 Exp Y6
The format of your answer will vary from calculator to calculator. Because the
answer to this question is in the normal range of numbers, the answer displayed
could be 850 000, so you have to change this to 8.5 105 . Other calculators may
automatically give the answer in scientific notation. If numbers are outside the range
of normal numbers, your calculator should display the answer in scientific notation.
Even when using a calculator, it is still important to be able to change from standard
form to scientific notation and vice-versa.

Activity:
1.

(a)

(b)

3.432 10 3 10

(c)

## 3.4 106 2.125 108

(d)

2.5 10 6 8.12 10 5

2.

## Perform the operations indicated by changing to scientific notation.

(a)

2000000000 0.00000003

(b)

0.00000045 0.00000000031

(c)

340000000000 0.000000125

(d)

Version 1

12

01/07/2010

Version 1

01/07/2010
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://fr.scribd.com/document/249042053/Topic-5-Operations-With-Numbers-in-Scientific-Notation", "fetch_time": 1582137071000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2020-10/segments/1581875144165.4/warc/CC-MAIN-20200219153707-20200219183707-00168.warc.gz", "warc_record_offset": 389079903, "warc_record_length": 82206, "token_count": 1415, "char_count": 4229, "score": 4.28125, "int_score": 4, "crawl": "CC-MAIN-2020-10", "snapshot_type": "latest", "language": "en", "language_score": 0.7871116399765015, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00043-of-00064.parquet"}