710 231 In Expanded Form

Expanded Note – The Fashion to Expand Numbers

What does Expanded Notation Mean?

Expanded note tin can exist defined as a fashion of expressing numbers by showing the value of each digit. Writing a number in expanded notation is not the same as writing in expanded form.

In expanded annotation, a number is represented equally the summation of each digit multiplied by its place value, whereas in expanded form, addition is only used between place value numbers. For case:

234 in expanded grade:

= 200 + 30 + 4

while 234 in expanded notation:

= (2 x 100) + (3 x 10) + (4 10 ane)

The original course of the number '234' is chosen a standard form.

How to do Expanded Notation?

To expand a item number (from its standard class), nosotros demand to aggrandize information technology into the sum of each digit multiplied by its matching identify value (ones, tens, hundreds, and so on).

These methods of writing a number in expanded notation and forms are illustrated in the examples below.

Example 1

Write 4,981 in expanded form?

Solution

The number four,981 can be written in expanded class as:

four,981 = 4,000 + 900 + eighty + 1
In this method, every number that comes later on a digit is replaced with zeros. For case, 4 and 9 in the number are represented as 4000 and 900 respectively.

Example 2

Write 15,807 in expanded form?

Solution

15,807 in expanded grade is represented equally:

fifteen,807 = 10,000 + 5,000 + 800 + 7
In this example, the place value of 0 in the number is zilch; therefore, the value in the tens digit is not represented because there are no tens.

Writing a number in expanded note entails showing the place of a number in exponential powers of ten.

Example three

Write the expanded notation of: four,981

Solution

iv,981 = (4 x 1,000) + (ix x 100) + (8 x ten) + (1 x i)

= (4 x 10 ^three) + (ix x ten ²) + (8 x x ¹) + ( i x x ⁰)

Example iv

Write 15,807 in expanded notation?

Solution

fifteen,807 = (one x ten,000) + (5 x 1,000) + (8 x 100) + (vii x 1)

= (ane x ten ⁴) + (5 x 10 ³) + (8 x 10 ²) + (7 x 10 ⁰)

Example 5

Write the thousands, hundreds, tens and ones for each of the following numbers:

a. 945

945 = 9 hundreds + iv tens + 7 ones

= 900 + 40 + five

b. 458

458= iv hundreds + 5 tens + 8 ones

= 400 + 50 + 8

c. 5973

5973 = 5 thousands + 9 hundreds + 7 tens + iii ones

= 5000 + 900 + 70 + 3

d. 333

333 = 3 hundreds + iii tens + 3 ones

= 300 + thirty + 3

e. 789

789 = 7 hundreds + 8 tens + 9 ones

= 700 + 80 + 9

Expanded Notation with Decimals

Decimal numbers can besides exist written in expanded notation by using exponential powers of x.

Example 5

Write 96. 24 in expanded note?

Solution

96.24 = 90 + 6 + 0.two + 0.04
(9 x ten) + (half dozen 10 one) + (3 x 10 ^-1) + (4 10 x ^-ii)

Case 6

Write the decimal number 536.072 in expanded note.

Solution

536.072 = 500 + 30 + 6 + 0.07 + 0.002
(v x x ^two) + (three ten 10 ¹) + (six ten 10 ⁰) + (7 x ten ^-ii) + (2 x ten ^-3)

Exercise Questions

i. Which of the post-obit shows the completely expanded annotation of the number, $90, 273$?

$90, 000 + 2000 + 70 + 3 $

$90, 000 + 200 + 70 + 3 $

$ninety, 000 + 200 + 73 $

$90, 000 + 2000 + 73$

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2. Which of the following shows the completely expanded notation of the number, $half-dozen, 587$?

$6, 000 + 800 + 70 + 5$

$six, 000 + 500 + 80 + seven$

$half-dozen, 000 + 80 + 57$

$6, 000 + 800 + l + vii$

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iii. Which of the post-obit shows the completely expanded notation of the number, $1, 234$?

$1, 000 + 200 + 40 + 3$

$i, 000 + 300 + 20 + 4$

$1, 000 + 200 + 34$

$ane, 000 + 200 + xxx + 4$

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4. Which of the following shows the completely expanded notation of the number, $29, 012$?

$twenty, 000 + ix, 000+ x + 2$

$twenty, 000 + nine, 000+ 100 + 12$

$20, 000 + 900+ 10 + 2$

$20, 000 + 900+ 12$

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v. Which of the post-obit shows the completely expanded note of the number, $49, 500$?

$49, 000 + 500$

$40, 000 + 9, 000+ 500$

$40, 000 + 9, 000+ 50$

$40, 000 + 900+ 50$

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6. Which of the following shows the completely expanded notation of the number, $4007$?

$4000+ k + 100+10+ 7$

$4000 + 100+10+ 7$

$4000 +10+ 7$

$4000 + 7$

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7. Which of the following shows the standard form of $50000 + 7000 + 900 + 60 + 1$?

$56, 791$

$567, 091$

$576, 091$

$57, 691$

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8. Which of the following shows the standard class of $6000 + 500 + xxx + 7$?

$six, 753$

$6, 537$

$6, 307$

$6, 357$

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9. Which of the post-obit shows the standard course of $20000 + k + 200 + 70 + 9$?

$22, 719$

$22, 179$

$21, 179$

$21, 279$

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10. Which of the following shows the standard form of $50000 + 7000 +x + 8$?

$57, 080$

$57, 018$

$57, 108$

$57, 180$

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11. Which of the post-obit shows the standard class of $400000 + 80 + viii$?

$40, 088$

$40, 808$

$400, 088$

$400, 808$

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12. Which of the following shows the standard form of $70000 + 7000 + x + ane$?

$71, 711$

$70, 711$

$77, 011$

$77, 110$

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thirteen. Truthful or False: The number, $1749$, when written in expanded class is equal to $yard + 700 + 40 +ix$.

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14. True or False: The number, $5605$, when written in expanded class is equal to $5000 + 600 + fifty + v$.

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xv. True or False: The number, $43453$, when written in expanded grade is equal to $4000+ 300+ 45 + 3$.

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16. True or Simulated: The number, $76125$, when written in expanded form is equal to $70000 + 6000 + 100 + 20 + 5$.

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17. True or Simulated: The number, $937032 $, when written in expanded grade is equal to $nine \text{ ten thousands} + 37 \text{ thousands} +3 \text{ hundreds} +ii \text{ i}$.

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