Mathematics requires solving difficulties that involve numbers. Us will work with whole numbers, i beg your pardon are any of the number 0, 1, 2, 3, and also so on. We first need to have actually a thorough expertise of the number system we use. Intend the researchers preparing a lunar command module understand it has to travel 382,564 kilometers to acquire to the moon. Just how well would they carry out if lock didn’t recognize this number? would it make much more of a difference if the 8 was off by 1 or if the 4 was off by 1?

In this section, you will take a look in ~ digits and also place value. Girlfriend will also learn just how to write totality numbers in words, standard form, and expanded form based ~ above the ar values of their digits.

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The Number System


A digit is one of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. All numbers are comprised of one or an ext digits. Number such as 2 have actually one digit, whereas numbers such as 89 have actually two digits. To know what a number yes, really means, you need to recognize what the digits stand for in a provided number.

The place of each digit in a number tells its value, or place value. We have the right to use a place-value chart like the one listed below to conveniently see the ar value for each digit. The location values because that the digits in 1,456 are displayed in this chart.


Place-Value Chart

Trillions

Billions

Millions

Thousands

Ones

1

4

5

6

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones


In the number 1,456, the number 1 is in the thousands place. The digit 4 is in the hundreds place. The number 5 is in the 10s place, and also the number 6 is in the people place.

As you see above, you deserve to tell a digit’s worth by looking in ~ its position. Look in ~ the variety of digits to the best of the digit, or create your number into a place-value chart, with the critical digit in the ones column. Both these techniques are shown in the example below.


Example

Problem

The advancement of a city over the past twenty years cost $962,234,532,274,312. What is the value of the number 6 in this number?


Place-Value Chart

Trillions

Billions

Millions

Thousands

Ones

9

6

2

2

3

4

5

3

2

2

7

4

3

1

2

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones


Write the number in the place-value chart. Review the worth of the 6 from the chart.

$962,234,532,274,312

60,000,000,000,000

Answer The worth of the number 6 is 60 trillion.



Below is an example with a number containing more digits. The words “million” and also “thousand” tell friend which durations the digits are in. The durations are separated by commas.


In a much away galaxy, there room 2,968,351,472 stars. What does the number 3 represent in this problem?

A) three hundred thousands

B) three hundreds

C) 3 hundred trillions

D) 3 hundred millions


Show/Hide Answer

A) three hundred thousands

Correct. The number 3 is in the hundreds thousands place.

B) three hundreds

Incorrect. The digit 4 is in the hundreds place. The exactly answer is three hundred thousands.

C) 3 hundred trillions

Incorrect. The number is less than a trillion, therefore this digit does not exist here. The correct answer is three hundred thousands.

D) three hundred millions

Incorrect. The number 9 is in the hundreds millions place. The correct answer is 3 hundred thousands.

Periods and also Standard Form


The standard form of a number describes a type of notation in i beg your pardon digits are separated into groups of 3 by commas. These teams of three digits are recognized as periods. Because that example, 893,450,243 has actually three periods with 3 digits in every period, as shown below.


Place-Value Chart

Trillions

Billions

Millions

Thousands

Ones

8

9

3

4

5

0

2

4

3

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones


Let’s research the number of digits and also periods in a better number. The variety of body cell in an typical adult human is about one hundreds trillion. This number is written as 100,000,000,000,000. An alert that there space 15 digits and 5 periods. Below is exactly how the number would certainly look in a place-value chart.


Place-Value Chart

Trillions

Billions

Millions

Thousands

Ones

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones


You are now acquainted with the place values of better numbers, so let’s examine a problem that requires converting native standard type to a native name.


Converting Standard form to indigenous Names


We often use indigenous names to create numbers. A word name for 42 is “forty-two.” The total variety of weeks in a year, 52, is written as “fifty-two.”

For totality numbers with three digits, use words “hundred” to define how countless hundreds there room in the number. For example, for the variety of days in a common year, 365, the number 3 is in the hundreds place. The word name because that the number is “three hundreds sixty-five.”

For whole numbers with four digits, begin the name with the variety of thousands, followed by the period name, together in the instance below.


Example

Problem

A guy owes $2,562 on a car. Write words name for this.

*

Answer

The word surname is two thousand, 5 hundred sixty-two.


For native names of better numbers, start at the left through the greatest period. For each period, write the one- to three-digit number in the period, and also then the period name. See the instance below.


Example

Problem

The building of a brand-new athletic facility cost $23,456,390. Write words name because that this number.

*

Answer

The word name is twenty-three million, 4 hundred fifty-six thousand, 3 hundred ninety.


Converting native Names to traditional Form


When convert word name to typical form, the word “thousand” speak you which duration the digits space in. Check out the example below.


Example

Problem

Forty-seven thousand, five hundred eighty-six blueberries are produced on a farm over the food of 3 years. Compose this number in standard form.

Forty-seven thousand

*

five hundred eighty-six

*
*

 Standard Notation is 47,586

Answer

The number in standard type is 47,586.

Example

Problem

There are three hundred eight million, six hundred thirty-two thousand, nine hundred seventy-eight bacteria in a sample the soil. Write this number in typical form.

*

Answer

The number in standard kind is 308,632,978.


Some number in word type may not cite a details period. For example, 3 million, one hundred twelve created in standard type is 3,000,112. Because the thousands duration is not mentioned, you would certainly write three zeros in the thousands period. You deserve to use a place-value chart to make it less complicated to check out the values of the digits. View the example below.


Example

Problem

A agency had a brand-new office structure constructed. The final cost was seventy-four million, three hundred sixty-two dollars. Write this number in typical form.


Place-Value Chart

Trillions

Billions

Millions

Thousands

Ones

7

4

0

0

0

3

6

 2

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones


*

Placing this number in a place- worth chart mirrors that the thousands duration is zero.

Remember to different each period with a comma.

Answer The number written in standard form is $74,000,362.


Writing numbers in expanded Form


Sometimes the is beneficial to compose numbers in A means to compose a number together a sum of the worth of that digits. For example, thirty-two is written in expanded kind as 30 + 2, or 3 tens + 2 ones, or (3 • 10) + (2 • 1).


")">expanded form
. In expanded form, the number is created as a amount of the worth of each digit.


Example

Problem

During the week, Mike cd driver a full of 264 miles. Compose 264 in broadened form.

First, determine the worth of each digit.

In numerical form:

264

200

264

60

264

4

In native form:

264

2 hundreds

264

6 tens

264

4 ones

Then, write the numbers together a sum.

Answer

264 written in expanded type is

200 + 60 + 4, or

2 hundreds + 6 10s + 4 ones, or

(2 • 100) + (6 • 10) + (4 • 1)


You can additionally use a place-value chart to assist write a number in increased form. Suppose the number of cars and also pick-up van in the U.S. In ~ this an extremely moment is 251,834,697. Location this number in a place-value chart.

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Place-Value Chart

Trillions

Billions

Millions

Thousands

Ones

2

5

1

8

3

4

6

9

7

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones


2 hundreds millions

200,000,000

+ 5 ten millions

+50,000,000

+ 1 million

+1,000,000

+ 8 hundreds thousands

+800,000

+ 3 ten thousands

+30,000

+ 4 thousands

+4,000

+ 6 hundreds

+600

+ 9 tens

+90

+ 7 ones

+7


Summary


Whole numbers the are higher than 9 covers multiple digits. Each digit in a offered number has actually a place value. To better understand location value, numbers can be put in a place-value graph so that the value of every digit have the right to be identified. Numbers with more than 3 digits have the right to be be separate into teams of 3 digits, recognized as periods. Any whole number can be to express in standard form, expanded form, or together a native name.