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Sample set e

Perform this subtraction.

503 -   37 ̲

The number 503 contains a single zero

  1. The number to the immediate left of 0 is 5. Decrease 5 by 1.

    5 1 = 4 size 12{5 - 1=4} {}

    503 - 37. The 5 is crossed out, with a 4 above it. The 0 is crossed out, with a 10 above it.

  2. Draw a line through the zero and make it a 10.
  3. Borrow from the 10 and proceed.

    503 - 37. The 5 is crossed out, with a 4 above it. The 0 is crossed out, with a 10 above it. The 10 is crossed out, with a 9 above it. The 3 is crossed out, with a 13 above it. The difference is 466.

    1 ten + 10 ones

    10 ones + 3 ones = 13 ones

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Practice set e

Perform each subtraction.

Borrowing from a group of zeros

Consider the problem 5000 -     37 ̲

In this case, we have a group of zeros.

Vertical subtraction. 5000 - 37 is equal to 5 thousands + 0 hundred + 0 tens + 0 ones, minus 3 tens + 7 ones.

Since we cannot borrow any tens or hundreds, we must borrow 1 thousand. One thousand = 10 hundreds.

Vertical subtraction. 4 thousands + 10 hundreds + 0 tens + 0 ones, minus 3 tens + 7 ones.

We can now borrow 1 hundred from 10 hundreds. One hundred = 10 tens.

Vertical subtraction. 4 thousands + 9 hundreds + 10 tens + 0 ones, minus 3 tens + 7 ones.

We can now borrow 1 ten from 10 tens. One ten = 10 ones.

Vertical subtraction. 4 thousands + 9 hundreds + 9 tens + 10 ones, minus 3 tens + 7 ones = 4 thousands + 9 hundreds + 6 tens + 3 ones, equal to 4,963

From observations made in this procedure we can suggest the following method for borrowing from a group of zeros.

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Borrowing from a group of zeros

To borrow from a group of zeros,
  1. Decrease the digit to the immediate left of the group of zeros by one.
  2. Draw a line through each zero in the group and make it a 9, except the rightmost zero, make it 10.
  3. Proceed to subtract as usual.

Sample set f

Perform each subtraction.

40,000 -     125 ̲

The number 40,000 contains a group of zeros.

  1. The number to the immediate left of the group is 4. Decrease 4 by 1.

    4 1 = 3 size 12{4 - 1=3} {}

  2. Make each 0, except the rightmost one, 9. Make the rightmost 0 a 10.

    40,000 - 125. Each digit of 40,000 is crossed out, and above it from left to right are the numbers, 3, 9, 9, 9, and 10.

  3. Subtract as usual.

    40,000 - 125. Each digit of 40,000 is crossed out, and above it from left to right are the numbers, 3, 9, 9, 9, and 10. The difference is 39,875.

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8,000,006 -       41,107 ̲

The number 8,000,006 contains a group of zeros.

  1. The number to the immediate left of the group is 8. Decrease 8 by 1.

    8 1 = 7 size 12{8 - 1=7} {}

  2. Make each zero, except the rightmost one, 9. Make the rightmost 0 a 10.

    8,000,006 - 41,107. All but the ones digit are crossed out, and above them from left to right are 7, 9, 9, 9, 9, and 10.

  3. To perform the subtraction, we’ll need to borrow from the ten.

    8,000,006 - 41,107. All but the ones digit are crossed out, and above them from left to right are 7, 9, 9, 9, 9, and 10. The 10 is crossed out, with a 9 above it. Above the 6 is a 16. The difference is 7,958,899.


    1 ten = 10 ones 10 ones + 6 ones = 16 ones

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Practice set f

Perform each subtraction.

21,007 -   4,873 ̲

16,134

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10,004 -   5,165 ̲

4,839

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16,000,000 -      201,060 ̲

15,789,940

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Calculators

In practice, calculators are used to find the difference between two whole numbers.

Sample set g

Find the difference between 1006 and 284.

Display Reads
Type 1006 1006
Press size 12{` - `} {} 1006
Type 284 284
Press = 722

The difference between 1006 and 284 is 722.

(What happens if you type 284 first and then 1006? We'll study such numbers in [link] Chapter 10.)

Practice set g

Use a calculator to find the difference between 7338 and 2809.

4,529

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Use a calculator to find the difference between 31,060,001 and 8,591,774.

22,468,227

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Exercises

For the following problems, perform the subtractions. You may check each difference with a calculator.

35,002 - 14,001 ̲

21,001

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5,000,566 - 2,441,326 ̲

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400,605 - 121,352 ̲

279,253

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77,893 -      421 ̲

77,472

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42,041 - 15,355 ̲

26,686

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64,000,002 -     856,743 ̲

63,143,259

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10,113 -   2,079 ̲

8,034

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92,526,441,820 - 59,914,805,253 ̲

32,611,636,567

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30,000 - 26,062 ̲

3,938

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9,000,003 -    726,048 ̲

8,273,955

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For the following problems, perform each subtraction.

Subtract 63 from 92.

The word "from" means "beginning at." Thus, 63 from 92 means beginning at 92, or 92 63 size 12{"92" - "63"} {} .
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Questions & Answers

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are you nano engineer ?
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fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
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That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
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is Bucky paper clear?
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so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
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Do you know which machine is used to that process?
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of graphene you mean?
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or in general
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in general
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Graphene has a hexagonal structure
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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