Place value to 10,000 and beyond

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課程筆記

What is Place Value?

Place value means the value of a digit depends on its position (place) in a number.
In the number 4,321, the digit 4 is in the thousands place, so it means 4,000.
Each place is worth ten times the place to its right. For example, 1 hundred = 10 tens.
The Hindu–Arabic numeral system (the one we use) is a base-ten system, using digits 0 to 9.
Numbers like 10,000 have a 1 in the ten-thousands place and zeros in the other places.

Reading and Writing Numbers

You can write numbers in numerals (like 5,678) or in words (like five thousand, six hundred seventy-eight).
Use a comma to separate thousands: 10,000 is ten thousand.
When writing in words, say the thousands, then the hundreds, then the tens and ones.
Example: 8,204 is eight thousand, two hundred four.
Practice with numbers up to 10,000 and beyond, like 12,345.

The Value of Each Digit

In 3,456, the digit 3 is in the thousands place, so its value is 3,000.
The digit 4 is in the hundreds place, so its value is 400.
The digit 5 is in the tens place, so its value is 50.
The digit 6 is in the ones place, so its value is 6.
A digit in one place is ten times the same digit in the place to its right. For example, in 2,222, the first 2 is 10 times the second 2.

Comparing and Ordering Numbers

Use < (less than) and > (greater than) to compare numbers.
To compare, look at the digits from left to right. The first place where they differ tells you which is bigger.
Example: 4,567 < 4,657 because 5 < 6 in the hundreds place.
Order numbers from smallest to largest or largest to smallest.
Remember: the alligator mouth opens toward the bigger number.

Rounding Numbers

Rounding means making a number simpler but close in value.
To round to the nearest 10, look at the ones digit. If it is 5 or more, round up; if 4 or less, round down.
To round to the nearest 100, look at the tens digit.
To round to the nearest 1,000, look at the hundreds digit.
Example: 3,472 rounded to the nearest 100 is 3,500 (because 7 in the tens place is 5 or more).

Counting and Finding More or Less

You can count in multiples of 10, 100, or 1,000.
To find 1,000 more than a number, add 1,000. To find 1,000 less, subtract 1,000.
Example: 1,000 more than 4,500 is 5,500.
Example: 1,000 less than 8,200 is 7,200.
Counting in multiples helps you see patterns in place value.

Negative Numbers on a Number Line

Negative numbers are less than zero, like -5.
You can see them on a number line to the left of zero.
An example is temperature: -10°C is colder than 0°C.
When counting backwards past zero, you go into negative numbers.
The further left on the number line, the smaller the number.

History of Place Value

The Babylonians used a base-60 system, which is why we have 60 minutes in an hour.
The Inca used knots in cords (quipu) to store numbers in a decimal system.
Roman numerals are not place value; they add values (like CCXXVIII = 228).
Our base-ten system came from India and spread through Arab mathematicians.
The decimal point (radix point) lets us write fractions like 3.5.

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1.What is the value of the digit 7 in the number 7,342?
Easy
- A7
- B70
- C700
- D7,000
2.In the number 5,678, the digit 6 is worth ten times the digit 6 in the number 6,000? (Think about place value.)
Easy
True or false?
3.Which number is the largest?
Easy
- A4,099
- B4,909
- C4,990
4.Put these numbers in order from smallest to largest.
Easy
- 3,210
- 3,021
- 3,102
- 3,201
5.Round 3,456 to the nearest hundred.
Medium
- A3,400
- B3,500
- C3,450
- D3,000
6.Round 8,721 to the nearest thousand.
Medium
- A8,000
- B9,000
- C8,700
- D8,800
7.The number 9,999 is greater than 10,000.
Medium
True or false?
8.Which of the following numbers are greater than 5,000? (Select all that apply.)
Medium
- A4,999
- B5,001
- C5,010
- D4,990
- E5,000

複習筆記

## Place Value to 10,000 and Beyond Place value means the value of a digit depends on its position in a number. In our number system, each place is worth ten times the place to its right. For example, in 4,567: - The 4 is in the thousands place: 4 × 1,000 = 4,000 - The 5 is in the hundreds place: 5 × 100 = 500 - The 6 is in the tens place: 6 × 10 = 60 - The 7 is in the ones place: 7 × 1 = 7 So 4,567 = 4,000 + 500 + 60 + 7. ### Reading and Writing Numbers - Write numbers in numerals (like 3,209) or in words (three thousand two hundred nine). - Use a comma to separate thousands: 10,000; 25,000; 100,000. ### Comparing and Ordering - Use < (less than) and > (greater than) to compare numbers. - Example: 3,456 < 3,465 because 3,456 has 5 tens and 3,465 has 6 tens. - Order numbers from smallest to largest or largest to smallest. ### Rounding - Round to the nearest 10: look at the ones digit. If it is 5 or more, round up; if less than 5, round down. Example: 47 rounds to 50 (ones digit 7 ≥ 5). - Round to the nearest 100: look at the tens digit. Example: 347 rounds to 300 (tens digit 4 < 5). - Round to the nearest 1,000: look at the hundreds digit. Example: 2,500 rounds to 3,000 (hundreds digit 5 ≥ 5). ### Counting and Finding More or Less - Count in multiples: 1,000; 2,000; 3,000; ... - Find 1,000 more or 1,000 less than a number. Example: 1,000 more than 4,500 is 5,500; 1,000 less is 3,500. ### Negative Numbers - Negative numbers are less than zero. They appear on a number line to the left of zero. - Example: Temperature can be -5°C (five degrees below zero). - Compare: -5 < -2 because -5 is further left on the number line. ### Key Idea A digit in one place is worth ten times the same digit in the place to its right. For example, in 5,555, the first 5 (thousands) is worth 10 times the second 5 (hundreds). Remember: Practice reading, writing, comparing, rounding, and finding more or less. Good luck on your exam!

Place value: The value of a digit depends on its position in a number. For example, in 3,456, the 4 is in the hundreds place and means 400.
Digit: A single symbol used to write numbers. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Ones: The place value of the rightmost digit. In 7, the 7 is in the ones place and means 7.
Tens: The place value to the left of ones. In 47, the 4 is in the tens place and means 40.
Hundreds: The place value to the left of tens. In 347, the 3 is in the hundreds place and means 300.
Thousands: The place value to the left of hundreds. In 4,567, the 4 is in the thousands place and means 4,000.
Compare: To decide if a number is greater than, less than, or equal to another number.
Less than (<): A symbol used to show that one number is smaller than another. For example, 3 < 5 means 3 is less than 5.
Greater than (>): A symbol used to show that one number is larger than another. For example, 7 > 2 means 7 is greater than 2.
Round: To change a number to a nearby number that is easier to use, like rounding 47 to 50 (nearest ten) or 347 to 300 (nearest hundred).
Negative number: A number less than zero, shown with a minus sign, like -5. It is used for temperatures below zero.
Number line: A line with numbers placed in order. Negative numbers are to the left of zero, and positive numbers are to the right.

字卡

What does the digit 7 represent in the number 7,342?

The digit 7 is in the thousands place, so it represents 7,000.

In the number 4,567, which digit is in the hundreds place?

The digit 5 is in the hundreds place.

Write the number 8,204 in expanded form.

8,204 = 8,000 + 200 + 4.

What is the value of the digit 3 in the number 13,456?

The digit 3 is in the thousands place, so it represents 3,000.

How many tens are in the number 5,670?

There are 7 tens, because the digit 7 is in the tens place.

What is the place value of the digit 9 in the number 9,000?

The digit 9 is in the thousands place, so its place value is thousands.

Compare: 4,321 and 4,312. Which is greater? Use < or >.

4,321 > 4,312 because 4,321 has 2 tens while 4,312 has 1 ten.

Order these numbers from least to greatest: 2,345; 2,435; 2,354.

2,345 < 2,354 < 2,435.

Round 3,678 to the nearest ten.

3,680 (because the ones digit is 8, so round up).

Round 5,432 to the nearest hundred.

5,400 (because the tens digit is 3, so round down).

Round 7,850 to the nearest thousand.

8,000 (because the hundreds digit is 8, so round up).

What is 1,000 more than 4,999?

5,999.

What is 1,000 less than 10,000?

9,000.

Count forward by 100s: 2,300; 2,400; 2,500; what comes next?

2,600.

What is the value of the digit 2 in the number 12,345?

The digit 2 is in the thousands place, so it represents 2,000.

Write the number 6,050 in words.

Six thousand fifty.

Write the number 'four thousand eight hundred two' in numerals.

4,802.

What is the smallest 5-digit number you can make using the digits 1, 0, 3, 5, 9 (use each once)?

10,359 (put the smallest non-zero digit first, then zero, then the rest in order).

What is the largest 4-digit number you can make using the digits 2, 7, 1, 9 (use each once)?

9,721 (put the digits in descending order).

On a number line, what number is exactly halfway between 5,000 and 6,000?

5,500.

If the temperature is -3°C and it drops 5°, what is the new temperature?

-8°C (because -3 - 5 = -8).

What is the value of the digit 0 in the number 10,000?

The zero is in the thousands place, so it represents 0 thousands (or just 0).

How many thousands are in the number 23,456?

23 thousands (the digit 2 is in the ten-thousands place, and 3 is in the thousands place, so 23 thousands).

What is the next number after 9,999?

10,000.

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