Standard form

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Tutor: Bilal

Summary

Standard form

​​In a nutshell

Standard index form (or standard form) is a convenient way of writing very large or very small numbers.



What does standard form look like?

A number is in standard index form if it is written in the form:

a×10ba\times10^b​​


Where the number aa​ is always between 11​ and 1010​, and bb​ is a whole number.



Writing a number in standard form

To write a number in standard index form, follow this procedure.

procedure

​​1.

Move the decimal point until the number is between 11 and 1010​. Count how many spaces the decimal point was moved.

2.

This number between 11​ and 1010​ is the value of aa​.

3.

The number of spaces the decimal point was moved is the value of bb​. If the decimal point moved to the left, then bb​ is positive. If the decimal point was moved to the right, then bb​ is negative.



Example 1

What is 7600076000 in standard index form?


First, write 7600076000 as 76000.0076000.00 and move the decimal point until the number is between 11and 1010​:

7.6 0 0 0 0 07\overset{\curvearrowleft \curvearrowleft \curvearrowleft \curvearrowleft}{.6\, 0\,0\,0\,}0\thinspace 0​, so a=7.6a=7.6


The decimal point moved 44 spaces to the left, so b=4b=4.

76000=7.6×104\underline{76000=7.6\times10^4}


Example 2

What is 0.00008150.0000815 in standard index form?


First, move the decimal point until the number is between 11 and 1010:

0 0 0 0 0 8.150\thinspace \overset{\curvearrowright \curvearrowright \curvearrowright \curvearrowright \curvearrowright}{0\,0\,0\,0\,8.}15​, so a=8.15a=8.15​​


The decimal point moved 55 spaces to the right, so b=5b=-5.


0.0000815=8.15×105\underline{0.0000815=8.15\times10^{-5}}



Multiplying and dividing in standard form

To multiply and divide two numbers in standard form, use your calculator to multiply the numbers. Then, make any adjustments if necessary to make sure the answer is in standard form.


Example 3

What is (1.5×108)×(9×103)(1.5\times10^8)\times(9\times10^{-3})?


Using the calculator gives:

(1.5×108)×(9×103)=1350000(1.5\times10^8)\times(9\times10^{-3})=1350000​​


Convert 13500001350000 into standard form:

1350000=1.35×1061350000=1.35\times10^6​​


(1.5×108)×(9×103)=1.35×106\underline{(1.5\times10^8)\times(9\times10^{-3})=1.35\times10^6}


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FAQs - Frequently Asked Questions

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