Mathematics involves solving difficulties that involve numbers. Us will work-related with whole numbers, i m sorry are any kind of of the numbers 0, 1, 2, 3, and also so on. We first need to have a thorough expertise of the number system we use. Mean the researchers preparing a lunar command module recognize it needs to travel 382,564 kilometers to obtain to the moon. Just how well would certainly they execute if they didn’t know this number? would it make an ext of a distinction if the 8 was off by 1 or if the 4 was off by 1?
In this section, you will take a look at digits and place value. Girlfriend will likewise learn how to write entirety numbers in words, traditional form, and also expanded type based on the ar values of their digits.
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The Number System
A digit is one of the signs 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. Every numbers are consisted of of one or more digits. Number such together 2 have one digit, whereas numbers such as 89 have actually two digits. To understand what a number really means, you require to recognize what the digits stand for in a given number.
The place of each digit in a number speak its value, or place value. We deserve to use a place-value chart favor the one below to quickly see the location value because that each digit. The place values for the number in 1,456 are presented 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 number 4 is in the hundreds place. The number 5 is in the 10s place, and the digit 6 is in the ones place.
As you see above, you can tell a digit’s worth by looking at its position. Look in ~ the variety of digits to the right of the digit, or write your number into a place-value chart, v the critical digit in the people column. Both these approaches are shown in the example below.
Example | ||||||||||||||
Problem | The breakthrough of a city over the past 20 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 native the chart.
$962,234,532,274,312
60,000,000,000,000
Answer The worth of the digit 6 is 60 trillion.
Below is an instance with a number containing an ext digits. The indigenous “million” and also “thousand” tell friend which durations the digits are in. The periods are separated by commas.
In a far away galaxy, there space 2,968,351,472 stars. What walk the digit 3 represent in this problem? A) three hundred thousands B) three hundreds C) three hundred trillions D) three hundred millions Show/Hide Answer A) three hundred thousands Correct. The number 3 is in the hundreds thousands place. B) 3 hundreds Incorrect. The number 4 is in the hundreds place. The correct answer is three hundred thousands. C) 3 hundred trillions Incorrect. The number is much less than a trillion, for this reason this number does not exist here. The exactly answer is 3 hundred thousands. D) 3 hundred millions Incorrect. The digit 9 is in the hundreds millions place. The exactly answer is 3 hundred thousands. Periods and also Standard Form The standard form of a number refers to a type of notation in i m sorry digits room separated into groups of three by commas. These groups of 3 digits are known as periods. For example, 893,450,243 has three periods with 3 digits in every period, as displayed below.
Let’s examine the number of digits and also periods in a higher number. The number of body cells in an average adult human being is about one hundred trillion. This number is written as 100,000,000,000,000. Notice that there are 15 digits and 5 periods. Below is how the number would look in a place-value chart.
You are now acquainted with the ar values of greater numbers, so let’s study a difficulty that requires converting from standard kind to a indigenous name.
Converting Standard type to native Names We frequently use word names to create numbers. A word name for 42 is “forty-two.” The total number of weeks in a year, 52, is written as “fifty-two.” For whole numbers with three digits, use the word “hundred” to explain how many hundreds there are in the number. Because that example, for the variety of days in a typical year, 365, the digit 3 is in the hundreds place. The word name for the number is “three hundred sixty-five.” For totality numbers with four digits, begin the name with the variety of thousands, adhered to by the period name, as in the example below.
For word names of better numbers, begin at the left with the greatest period. Because that each period, create the one- come three-digit number in the period, and then the duration name. View the example below.
Converting native Names to standard Form When converting word surname to standard form, the word “thousand” tells you which duration the digits room in. See the example below.
five hundred eighty-six
Standard Notation is 47,586 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Answer | The number in standard kind is 47,586. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Example | ||
Problem | There are three hundreds eight million, 6 hundred thirty-two thousand, nine hundred seventy-eight bacteria in a sample of soil. Write this number in standard form. | |
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Answer | The number in standard type is 308,632,978. | |
Some numbers in word form may not point out a particular period. For example, 3 million, one hundred twelve created in standard form is 3,000,112. Since the thousands period is not mentioned, you would write 3 zeros in the thousands period. You deserve to use a place-value chart to make it much easier to see the worths of the digits. See the example below.
Example |
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Problem | A company had a new office structure constructed. The final cost was seventy-four million, three hundred sixty-two dollars. Compose 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 shows that the thousands period is zero.
Remember to different each duration with a comma.
Answer The number created in standard form is $74,000,362.
Writing number in broadened Form
Sometimes the is advantageous to compose numbers in A means to create a number together a amount of the value of that is digits. For example, thirty-two is created in expanded type as 30 + 2, or 3 10s + 2 ones, or (3 • 10) + (2 • 1).
")">expanded form. In expanded form, the number is composed as a sum of the value of each digit.
Example | ||||
Problem | During the week, Mike cd driver a complete of 264 miles. Create 264 in expanded form. | |||
First, recognize the worth of every digit. In numerical form: | ||||
264 | 200 | |||
264 | 60 | |||
264 | 4 | |||
In word form: | ||||
264 | 2 hundreds | |||
264 | 6 tens | |||
264 | 4 ones | |||
Then, create the numbers together a sum. | ||||
Answer | 264 composed in expanded type is 200 + 60 + 4, or 2 hundreds + 6 tens + 4 ones, or (2 • 100) + (6 • 10) + (4 • 1) | |||
You can also use a place-value graph to assist write a number in expanded form. Mean the variety of cars and also pick-up trucks 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 that are better than 9 consists multiple digits. Each digit in a offered number has a location value. To better understand location value, numbers have the right to be placed in a place-value graph so that the value of every digit deserve to be identified. Number with more than three digits have the right to be separated into teams of three digits, well-known as periods. Any whole number have the right to be express in traditional form, increased form, or as a word name.