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Scientific Notation
07/26/12 lntaylor ©
Table of Contents
Learning Objectives
Writing numbers in Standard Notation
Writing numbers in Scientific Notation
Practice
07/26/12 lntaylor ©
LO1:
LO2:
Define and differentiate standard and scientific notation
Rewrite notations in different forms
07/26/12 lntaylor ©TOC
Learning Objectives
Def1:
Def2:
Standard Notation is the normal way of writing any numberusing decimals and commas
Scientific Notation is the scientific was of writing very largeand very small numbers using a non zero digit followed by adecimal multiplied by a 10 with an exponent
07/26/12 lntaylor ©TOC
Definitions
PK1: Knowledge of mathematical place holders
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Previous Knowledge
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100 millions
10 millions
1 millions
100 thousands
10 thousands
1 thousands
Hundreds
Tens
Ones
Decimal
Tenths
Hundredths
Thousandths
9 8 7 , 6 5 4 , 3 2 1 . 9 8 7
Standard Notation
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Three thousand six hundred and fifty three
Step 1 Write the number above in Standard Notation
07/26/12 lntaylor ©TOC
3,653
Now you try
Five hundred and fifty million, six hundred thousand and four one-hundreds
07/26/12 lntaylor ©TOC
Five hundred and fifty million, six hundred thousand and four one-hundreds
Step 1 Write the number above in Standard Notation
07/26/12 lntaylor ©TOC
550,600,000.04
Now you try
Five hundred and seven thousandths
07/26/12 lntaylor ©TOC
Five hundred and seven thousandths
Step 1 Write the number above in Standard Notation
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0.507
Scientific Notation
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Three thousand six hundred and fifty three
Step 1 Write the number above in Standard Notation first
07/26/12 lntaylor ©TOC
3,653
Step 2 Rewrite the number with TWO decimalsFind the first non zero digit and put a decimal after itLeave the existing decimal in place
Step 3 Write the first non zero digit number followed by a decimal
3.
Step 4 Write the rest of the numbers to the right of the decimal
653
Step 5 Write a X 10
x 10
Step 6 Count the numbers between the decimals
3
Step 7 That number becomes the exponent
=
3.653.
Now you try
Five hundred and fifty million, six hundred thousand and four one-hundreds
07/26/12 lntaylor ©TOC
Five hundred and fifty million, six hundred thousand and four one-hundreds
Step 1 Write the number above in Standard Notation first
07/26/12 lntaylor ©TOC
550,600.04
Step 2 Rewrite the number with TWO decimalsFind the first non zero digit and put a decimal after itLeave the existing decimal in place
Step 3 Write the first non zero digit number followed by a decimal
5.
Step 4 Write the rest of the numbers to the right of the decimal
5060004
Step 5 Write a X 10
x 10
Step 6 Count the numbers between the decimals
5
Step 7 That number becomes the exponent
=
5.50600.04
Now you try
Five hundred and seven thousandths
07/26/12 lntaylor ©TOC
Five hundred and seven thousandths
Step 1 Write the number above in Standard Notation first
07/26/12 lntaylor ©TOC
0.507
Step 2 Rewrite the number with TWO decimalsFind the first non zero digit and put a decimal after itLeave the existing decimal in place
Step 3 Write the first non zero digit number followed by a decimal
5.
Step 4 Write the rest of the numbers to the right of the decimal
07
Step 5 Write a X 10
x 10
Step 6 Count the numbers between the decimals
-1
Step 7 That number becomes the exponent
=
.5.07
Step 8 Remember that a negative exponent means the standard number is between 0 and 1
Practice
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07/26/12 lntaylor ©TOC
Standard Notation Scientific Notation
3,459,876.987
912
0.876560001
0.000000605
10
1
> 3.459876987 x 10 6
>
>
>
>
>
9.12 x 10 2
8.76560001 x 10 -1
6.05 x 10 - 7
1.0 x 10 1
1.0 x 10 0
clear answers
07/26/12 lntaylor ©TOC
Scientific Notation Standard Notation
3.473 x 107
- 9.12 x 10 -5
7.60001 x 105
6.05 x 10 -7
1.0 x 10 -1
9.0567 x 100
>
>
>
>
>
>
34,730,000
- 0.0000912
760,001
0.000000605
0.1
9.0567
clear answers
