what is the name of the number 10 to the power of 3?

Place Value and Names for Whole Numbers

Learning Objective(s)

· Find the place value of a digit in a whole number.

· Write a whole number in words and in standard form.

· Write a whole number in expanded course.

Introduction

In this section, y'all will have a await at digits and place value. You will also learn how to write whole numbers in words, standard course, and expanded course based on the place values of their digits.

The Number Organization

A digit is ane of the symbols 0, 1, ii, three, 4, five, 6, 7, 8, or nine. All numbers are made up of one or more than digits. Numbers such as 2 accept one digit, whereas numbers such as 89 have two digits. To understand what a number really ways, you lot demand to understand what the digits represent in a given number.

The position of each digit in a number tells its value, or identify value. We can apply a identify-value chart similar the one below to easily meet the place value for each digit. The place values for the digits in 1,456 are shown in this chart.

Identify-Value Chart

Trillions

Billions

Millions

Thousands

Ones

1

4

5

half-dozen

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

In the number i,456, the digit 1 is in the thousands place. The digit 4 is in the hundreds place. The digit 5 is in the tens identify, and the digit 6 is in the ones place.

As you see above, y'all tin tell a digit'southward value by looking at its position. Await at the number of digits to the right of the digit, or write your number into a place-value nautical chart, with the terminal digit in the ones column. Both these methods are shown in the case beneath.

Example
Problem	The evolution of a city over the past twenty years cost $962,234,532,274,312. What is the value of the digit 6 in this number?
Identify-Value Nautical chart Trillions Billions Millions Thousands Ones 9 six 2 2 3 4 5 iii 2 2 vii 4 3 one 2 Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones		Write the number in the place-value chart. Read the value of the vi from the chart.
$9 half dozen 2,234,532,274,312 60,000,000,000,000
Answer The value of the digit 6 is 60 trillion.

In a far away galaxy, there are 2,968,351,472 stars. What does the digit 3 represent in this trouble?

A) three hundred thousands

B) iii hundreds

C) three hundred trillions

D) iii hundred millions

Show/Hibernate Respond

A) three hundred thousands

Correct. The digit 3 is in the hundred thousands identify.

B) three hundreds

Wrong. The digit four is in the hundreds place. The correct answer is 3 hundred thousands.

C) three hundred trillions

Incorrect. The number is less than a trillion, then this digit does not be here. The correct respond is three hundred thousands.

D) three hundred millions

Incorrect. The digit nine is in the hundred millions identify. The correct respond is three hundred thousands.

Periods and Standard Form

The standard form of a number refers to a type of notation in which digits are separated into groups of three by commas. These groups of three digits are known equally periods. For example, 893,450,243 has three periods with iii digits in each menstruation, as shown below.

Place-Value Chart

Trillions

Billions

Millions

Thousands

Ones

eight

9

3

4

5

0

2

four

3

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Let's examine the number of digits and periods in a greater number. The number of trunk cells in an average adult human is most one hundred trillion. This number is written equally 100,000,000,000,000. Find that there are fifteen digits and 5 periods. Here is how the number would look in a place-value nautical chart.

Place-Value Nautical 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 lot are now familiar with the place values of greater numbers, so let's examine a problem that involves converting from standard class to a word proper noun.

Converting Standard Form to Word Names

We ofttimes use word names to write numbers. A word proper name for 42 is "forty-two." The full number of weeks in a twelvemonth, 52, is written equally "fifty-two."

For whole numbers with iii digits, use the word "hundred" to describe how many hundreds there are in the number. For example, for the number of days in a normal year, 365, the digit 3 is in the hundreds identify. The word name for the number is "iii hundred sixty-5."

For whole numbers with iv digits, begin the proper noun with the number of thousands, followed by the period proper name, equally in the example beneath.

Case
Trouble		A human owes $2,562 on a motorcar. Write the word proper name for this.
Respond	The word name is two thousand, v hundred sixty-ii.

For word names of greater numbers, begin at the left with the greatest menstruum. For each menstruation, write the one- to iii-digit number in the period, and then the flow name. Come across the case below.

Example
Problem		The construction of a new athletic heart price $23,456,390. Write the discussion proper name for this number.
Reply	The word name is 20-three 1000000, four hundred fifty-six thousand, three hundred xc.

Converting Word Names to Standard Class

When converting discussion names to standard form, the word "thousand" tells you which period the digits are in. See the instance beneath.

Example
Trouble		Twoscore-7 1000, five hundred eighty-six blueberries are produced on a farm over the course of 3 years. Write this number in standard course.
Forty-7 chiliad Five hundred 80-six  Standard Note is 47,586
Answer	The number in standard form is 47,586.

Below is an example with a number containing more digits. The words "one thousand thousand" and "thousand" tell you lot which periods the digits are in. The periods are separated past commas.

Case
Problem		There are iii hundred eight 1000000, six hundred thirty-ii m, nine hundred seventy-eight leaner in a sample of soil. Write this number in standard form.
Reply	The number in standard form is 308,632,978.

Some numbers in word grade may non mention a specific menses. For example, iii one thousand thousand, ane hundred twelve written in standard form is 3,000,112. Considering the thousands period is non mentioned, y'all would write three zeros in the thousands menstruation. You lot tin use a identify-value chart to brand it easier to see the values of the digits. Encounter the case below.

Instance
Problem	A company had a new office edifice constructed. The concluding cost was seventy-4 million, 3 hundred sixty-two dollars. Write this number in standard course.
Identify-Value Nautical chart Trillions Billions Millions Thousands Ones 7 4 0 0 0 3 vi  two Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones		Placing this number in a place- value nautical chart shows that the thousands period is cipher. Remember to split up each catamenia with a comma.
Respond The number written in standard form is $74,000,362.

Writing Numbers in Expanded Form

Sometimes it is useful to write numbers in expanded form. In expanded course, the number is written every bit a sum of the value of each digit.

Example
Trouble		During the week, Mike drives a full of 264 miles. Write 264 in expanded class.
First, identify the value of each digit. In numerical form:
2 64			200
2 6 4			threescore
26 four			4
In give-and-take class:
2 64			2 hundreds
two six 4			half dozen tens
26 iv			4 ones
And so, write the numbers as a sum.
Answer	264 written in expanded form is 200 + lx + 4, or 2 hundreds + 6 tens + 4 ones, or (two • 100) + (6 • 10) + (4 • one)

You lot can as well use a place-value nautical chart to help write a number in expanded class. Suppose the number of cars and pick-up trucks in the U.Due south. at this very moment is 251,834,697. Place this number in a identify-value chart.

Place-Value Nautical chart

Trillions

Billions

Millions

Thousands

Ones

2

five

1

eight

iii

4

6

nine

7

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

ii hundred millions	200,000,000
+ 5 ten millions	+fifty,000,000
+ i million	+1,000,000
+ 8 hundred thousands	+800,000
+ 3 ten thousands	+30,000
+ four thousands	+4,000
+ 6 hundreds	+600
+ ix tens	+ninety
+ 7 ones	+seven

Summary

Whole numbers that are greater than ix consist of multiple digits. Each digit in a given number has a place value. To improve understand place value, numbers can be put in a place-value chart then that the value of each digit can be identified. Numbers with more than three digits can be separated into groups of 3 digits, known equally periods. Any whole number can be expressed in standard form, expanded form, or as a give-and-take name.

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Source: http://montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT_RESOURCE/U01_L1_T1_text_final.html

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