Place value to a million and rounding

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Apuntes de la lección

Place Value to a Million

Place value is the value of a digit based on its position in a number.
In the number 1,234,567, the digit 1 is in the millions place, so it means 1,000,000.
The digit 2 is in the hundred thousands place, so it means 200,000.
The digit 3 is in the ten thousands place, so it means 30,000.
The digit 4 is in the thousands place, so it means 4,000.
The digit 5 is in the hundreds place, so it means 500.
The digit 6 is in the tens place, so it means 60.
The digit 7 is in the ones place, so it means 7.

Reading and Writing Numbers to a Million

To read a large number, split it into groups of three digits from the right: 1,234,567.
Read each group and say its name: one million, two hundred thirty-four thousand, five hundred sixty-seven.
When writing numbers in words, use a hyphen for numbers from 21 to 99 (like twenty-one).
Use commas to separate groups of three digits in numbers of 1,000 or more.
The number 1,000,000 is one million, and 999,999 is nine hundred ninety-nine thousand, nine hundred ninety-nine.

Comparing and Ordering Numbers

To compare numbers, look at the digits from left to right.
The number with more digits is larger (e.g., 1,000,000 > 999,999).
If two numbers have the same number of digits, compare the first digit that is different.
Use the symbols < (less than), > (greater than), and = (equal to) to show comparison.
To order numbers, write them from smallest to largest (ascending) or largest to smallest (descending).

Decimals to Thousandths

A decimal is a number with a decimal point, like 0.5 or 3.142.
The first digit after the decimal point is the tenths place.
The second digit after the decimal point is the hundredths place.
The third digit after the decimal point is the thousandths place.
In 0.375, the digit 3 is in the tenths place, 7 is in the hundredths place, and 5 is in the thousandths place.

Writing Decimals in Expanded Form

Expanded form shows the value of each digit in a number.
For a decimal like 0.375, expanded form is 0.3 + 0.07 + 0.005.
For a whole number like 4,302, expanded form is 4,000 + 300 + 2.
You can also write expanded form using fractions: 0.375 = 3/10 + 7/100 + 5/1000.
Expanded form helps you understand the value of each digit.

Comparing Decimals

To compare decimals, line up the decimal points and compare digits from left to right.
If one decimal has fewer digits, you can add zeros to the right to make them the same length.
For example, 0.5 is greater than 0.45 because 0.50 > 0.45.
Use <, >, or = to compare decimals.
Ordering decimals is like ordering whole numbers, but you compare the decimal parts.

Rounding Whole Numbers

Rounding means making a number simpler but close to its original value.
To round to the nearest ten, look at the ones digit. If it is 5 or more, round up; if it is 4 or less, round down.
Example: 47 rounded to the nearest ten is 50, because the ones digit is 7 (5 or more).
To round to the nearest hundred, look at the tens digit.
Example: 1,234 rounded to the nearest hundred is 1,200, because the tens digit is 3 (less than 5).

Rounding Decimals

To round a decimal to the nearest tenth, look at the hundredths digit.
If the hundredths digit is 5 or more, round up the tenths digit; if it is 4 or less, keep the tenths digit the same.
Example: 3.47 rounded to the nearest tenth is 3.5, because the hundredths digit is 7.
To round to the nearest hundredth, look at the thousandths digit.
Example: 0.375 rounded to the nearest hundredth is 0.38, because the thousandths digit is 5.

Counting in Powers of 10

Powers of 10 are numbers like 10, 100, 1,000, 10,000, 100,000, and 1,000,000.
Counting forwards in powers of 10 means adding 10, 100, 1,000, etc.
Counting backwards means subtracting those amounts.
Example: Counting backwards by 100 from 1,000: 1,000, 900, 800, 700, 600.
You can also count through zero into negative numbers, like -10, -20, -30.

Roman Numerals to 1,000

Roman numerals are an old way of writing numbers using letters: I, V, X, L, C, D, M.
I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000.
To write a number, combine these symbols. If a smaller number comes before a larger one, subtract it (like IV = 4).
If a smaller number comes after a larger one, add it (like VI = 6).
Example: 49 is written as XLIX (40 + 9).

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Preguntas de práctica

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1.What is the value of the digit 7 in the number 3,742,105?
Easy
- A700,000
- B70,000
- C7,000
- D700
2.Which of these numbers is the largest?
Easy
- A456,789
- B456,798
- C456,897
- D456,978
3.The number 1,000,000 has 7 digits.
Easy
True or false?
4.Which number is equal to 5,000,000 + 40,000 + 300 + 2?
Medium
- A5,040,302
- B5,400,302
- C5,004,302
- D5,040,032
5.Which of the following numbers are less than 1,000,000? (select all that apply)
Easy
- A999,999
- B1,000,001
- C999,999.9
- D1,000,000.0
6.Put these numbers in order from smallest to largest.
Medium
- 345,678
- 345,768
- 345,687
- 345,876
7.When rounding 2,345,678 to the nearest hundred thousand, you get 2,300,000.
Easy
True or false?
8.A school has 1,234,567 books in its library. If you round this number to the nearest ten thousand, what do you get?
Medium
- A1,230,000
- B1,240,000
- C1,200,000
- D1,300,000

Más preguntas

9.Which symbol makes this sentence true: 456,789 ___ 456,879
Easy
- A<
- B>
- C=
- D≈
10.Match each digit to its place value in the number 6,482,913.
Easy
- 4
- 8
- 2
- 9
- hundred thousands
- ten thousands
- hundreds
- tens
11.Arrange these numbers from smallest to largest: 987,654; 978,654; 987,465; 987,546.
Medium
- 987,654
- 978,654
- 987,465
- 987,546
12.Which of these numbers round to 2,000,000 when rounded to the nearest million? (Select all that apply)
Medium
- A1,499,999
- B1,500,000
- C2,499,999
- D2,500,000
- E1,999,999
13.What is 3,456,789 rounded to the nearest ten thousand?
Medium
- A3,400,000
- B3,450,000
- C3,460,000
- D3,500,000
14.Which digit is in the hundred thousands place in the number 5,678,912?
Easy
- A5
- B6
- C7
- D8
15.Match each number to its value when rounded to the nearest thousand.
Medium
- 12,499
- 12,500
- 13,499
- 13,500
- 12,000
- 13,000
- 13,000
- 14,000
16.Arrange these numbers from smallest to largest: 0.5, 0.05, 0.55, 0.505.
Medium
- 0.5
- 0.05
- 0.55
- 0.505
17.What is the value of the digit 3 in the number 3,250,000?
Easy
- A3
- B30
- C3,000,000
- D300,000
18.Which number is written correctly in words?
Easy
- AFour hundred fifty thousand two hundred
- BFour hundred and fifty thousand and two hundred
- CFour hundred fifty thousand two hundred and
19.Round 784,562 to the nearest ten thousand.
Medium
- A780,000
- B790,000
- C800,000
- D784,000
20.Which of the following numbers round to 3,500,000 when rounded to the nearest hundred thousand? (Select all that apply)
Medium
- A3,450,000
- B3,550,000
- C3,449,999
- D3,540,000
- E3,460,000
21.Put these numbers in order from smallest to largest: 0.5, 0.05, 0.55, 0.505.
Medium
- 0.5
- 0.05
- 0.55
- 0.505
22.A baker sells 1,234,567 cupcakes in a year. If she rounds this number to the nearest hundred thousand, what is the rounded number?
Medium
- A1,200,000
- B1,300,000
- C1,230,000
- D1,240,000
23.A zoo has 2,456,789 visitors last year. The manager wants to report the number rounded to different places. Which of the following statements are true? (Select all that apply)
Medium
- ARounded to the nearest thousand: 2,457,000
- BRounded to the nearest ten thousand: 2,460,000
- CRounded to the nearest hundred thousand: 2,500,000
- DRounded to the nearest million: 2,000,000
- ERounded to the nearest ten: 2,456,790
24.The number 5,999,999 rounded to the nearest million is 6,000,000.
Easy
True or false?
25.Match each number to its value when rounded to the nearest hundred thousand.
Medium
- 2,456,789
- 2,543,210
- 2,499,999
- 2,500,000
- 2,500,000
- 2,500,000
26.A number is rounded to the nearest ten thousand and the result is 450,000. Which of the following could be the original number?
Medium
- A449,999
- B444,999
- C455,000
- D445,000
27.A store sells 3,456,789 items in a year. The owner says, 'We sold about 3,500,000 items.' Which of the following statements are true? (Select all that apply)
Hard
- AThe owner rounded to the nearest hundred thousand.
- BThe owner rounded to the nearest million.
- CThe exact number is 3,456,789.
- DThe rounded number is less than the exact number.
- EThe rounded number is greater than the exact number.
28.Rounding 2,500,000 to the nearest million gives 3,000,000.
Easy
True or false?
29.Arrange these numbers from largest to smallest.
Medium
- 3,456,789
- 3,456,798
- 3,465,789
- 3,546,789
30.A company has 2,345,678 employees. If they round this number to the nearest ten thousand, what is the result?
Medium
- A2,300,000
- B2,350,000
- C2,340,000
- D2,400,000
31.Match each number to the place value of the digit 6.
Medium
- 6,000,000
- 1,600,000
- 1,060,000
- millions
- hundred thousands
- ten thousands
32.The number 4,500,000 rounded to the nearest hundred thousand is 4,500,000.
Medium
True or false?
33.What is the value of the digit 5 in the number 5,678,912?
Easy
- A5
- B5,000,000
- C500,000
- D50,000
34.Which number is the same as 7,000,000 + 200,000 + 30,000 + 400 + 5?
Easy
- A7,230,405
- B7,203,405
- C7,230,450
- D7,203,450
35.Match each number to its value when rounded to the nearest hundred.
Easy
- 1,234
- 1,249
- 1,250
- 1,200
- 1,200
- 1,300
36.Which symbol makes this sentence true: 456,789 ___ 456,879?
Medium
- A<
- B>
- C=
- D≈
37.Which of the following numbers rounds to 2,000,000 when rounded to the nearest million?
Medium
- A1,499,999
- B1,500,000
- C2,499,999
- D2,500,000
38.Match each number to the place value of the digit 5.
Medium
- 5,123,456
- 1,235,456
- 1,253,456
- 1,234,565
- hundred thousands
- ten thousands
- hundreds
- ones
39.Arrange these numbers from smallest to largest.
Easy
- 999,999
- 1,000,000
- 999,990
- 1,000,001
40.Which of the following numbers round to 5,000,000 when rounded to the nearest million? (Select all that apply)
Medium
- A4,500,000
- B4,499,999
- C5,499,999
- D5,500,000
41.Round 847,362 to the nearest thousand.
Easy
42.Write the number 902,001 in expanded form.
Easy
____ + ____ + ____
43.What is the place value of the digit 4 in the number 4,567,890?
Easy
44.A city has a population of 4,876,210. If you round this to the nearest hundred thousand, what is the result?
Medium
45.Write the missing number.
Medium
The number 8,500,000 is 8 million plus ____ hundred thousand.
46.What is the value of the digit 9 in the number 4,950,000? Write your answer in words.
Easy
47.What is 5,678,912 rounded to the nearest ten thousand?
Medium
48.What is the value of the digit 8 in the number 4,876,210?
Easy
49.Round 3,456,789 to the nearest hundred thousand.
Medium
50.Write the number 900,400,003 in words.
Easy
51.A number has a 7 in the ten thousands place, a 3 in the hundred thousands place, and a 9 in the ones place. All other digits are zero. What is the number?
Medium
52.Round 7,849,321 to the nearest ten thousand.
Medium
53.Explain why rounding 3,456,789 to the nearest ten thousand gives 3,460,000.
Medium
54.Explain why rounding 3,456,789 to the nearest ten thousand gives 3,460,000, but rounding to the nearest hundred thousand gives 3,500,000.
Hard
55.Explain why rounding 4,567,890 to the nearest hundred thousand gives 4,600,000.
Medium
56.Round 847,362 to the nearest thousand.
Easy
- A847000
- B1016400
- C762300
- D931700
57.A city has a population of 4,876,210. If you round this to the nearest hundred thousand, what is the result?
Medium
- A4410000
- B5880000
- C5390000
- D4900000
58.What is 5,678,912 rounded to the nearest ten thousand?
Medium
- A5112000
- B6248000
- C6816000
- D5680000
59.What is the value of the digit 8 in the number 4,876,210?
Easy
- A960000
- B720000
- C800000
- D880000
60.Round 3,456,789 to the nearest hundred thousand.
Medium
- A3150000
- B3850000
- C3500000
- D4200000
61.A number has a 7 in the ten thousands place, a 3 in the hundred thousands place, and a 9 in the ones place. All other digits are zero. What is the number?
Medium
- A407010
- B444011
- C370009
- D333008
62.Round 7,849,321 to the nearest ten thousand.
Medium
- A8635000
- B9420000
- C7850000
- D7065000

Apuntes de repaso

## Place Value to a Million and Rounding ### Place Value to a Million - **Place value** tells you the value of each digit in a number. For example, in 345,678, the digit 4 is in the ten-thousands place, so it means 40,000. - **Digits** are the symbols 0-9. A number like 1,000,000 has 7 digits. - **Expanded form** shows the value of each digit: 345,678 = 300,000 + 40,000 + 5,000 + 600 + 70 + 8. - **Comparing numbers**: Use < (less than), > (greater than), or = (equal to). Compare digits from left to right. - **Ordering**: Put numbers in order from smallest to largest or largest to smallest. - **Decimals**: Read and write decimals to thousandths. For example, 0.375 is three hundred seventy-five thousandths. ### Rounding - **Rounding** means changing a number to a nearby, simpler number. For example, 23.4476 rounded to two decimal places is 23.45. - **Rounding whole numbers**: Look at the digit to the right of the place you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down. For example, round 123,456 to the nearest thousand: look at the hundreds digit (4), so 123,000. - **Rounding decimals**: Same rule. Round 3.14159 to the nearest hundredth: look at the thousandths digit (1), so 3.14. - **Rounding to a given place**: You can round to any place, like tens, hundreds, or tenths. - **Wavy equals sign (≈)** means "is approximately equal to". For example, 9.98 ≈ 10. - **Why round?** To make numbers easier to report or understand. For example, if a number is 123,456 but only accurate to the nearest hundred, it is better to say "about 123,500". - **Rounding errors**: When you round, you lose some exactness. In long calculations, errors can add up. ### Key Tips - Always identify the place value you are rounding to. - Look at the digit immediately to the right. - If that digit is 5 or more, round up; if 4 or less, round down. - Practice with big numbers and decimals!

Place value: The value of a digit based on its position in a number. For example, in 345,678, the 4 is in the ten-thousands place, so it means 40,000.
Digit: A single symbol used to make numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.
Expanded form: A way to write a number that shows the value of each digit. For example, 345,678 = 300,000 + 40,000 + 5,000 + 600 + 70 + 8.
Rounding: Changing a number to a nearby, simpler number. For example, 23.4476 rounded to two decimal places is 23.45.
Approximately equal to (≈): A symbol that means 'is about'. For example, 9.98 ≈ 10.
Round up: To increase the digit in the place you are rounding to by 1, when the digit to the right is 5 or more.
Round down: To keep the digit in the place you are rounding to the same, when the digit to the right is 4 or less.

Tarjetas

What is the value of the digit 7 in the number 3,475,209?

The digit 7 is in the ten-thousands place, so its value is 70,000.

Write the number 2,304,567 in expanded form.

2,000,000 + 300,000 + 0 + 4,000 + 500 + 60 + 7.

Compare: 456,789 ___ 456,798. Use <, >, or =.

456,789 < 456,798 because 789 is less than 798.

What is the value of the digit 5 in the number 0.25?

The digit 5 is in the hundredths place, so its value is 5 hundredths (0.05).

Write the decimal 0.307 in words.

Three hundred seven thousandths.

Round 3,456 to the nearest hundred.

3,500. The tens digit is 5, so round up.

Round 12.345 to the nearest tenth.

12.3. The hundredths digit is 4, so round down.

What does the symbol ≈ mean?

It means 'approximately equal to'. For example, 9.98 ≈ 10.

Round 999,999 to the nearest ten thousand.

1,000,000. The thousands digit is 9, so round up.

Write the number 1,000,000 in words.

One million.

What is the place value of the digit 4 in 0.004?

The digit 4 is in the thousandths place, so its value is 4 thousandths (0.004).

Order these numbers from least to greatest: 234,567; 234,576; 234,567.

234,567; 234,567; 234,576. (If duplicates, list both.)

Round 0.999 to the nearest hundredth.

1.00. The thousandths digit is 9, so round up.

What is the value of the digit 0 in 5,000,000?

Each zero is in a place with value 0, so the digit 0 has a value of 0.

Write 0.5 as a fraction in simplest form.

1/2.

Compare: 0.7 ___ 0.70. Use <, >, or =.

They are equal, so 0.7 = 0.70.

Round 12,345 to the nearest thousand.

12,000. The hundreds digit is 3, so round down.

What is the place value of the digit 8 in 8,000,000?

It is in the millions place, so its value is 8,000,000.

Write 0.25 as a fraction in simplest form.

1/4.

Round 3.14159 to the nearest thousandth.

3.142. The ten-thousandths digit is 5, so round up.

What is the value of the digit 6 in 0.06?

The digit 6 is in the hundredths place, so its value is 6 hundredths (0.06).

Round 1,234,567 to the nearest million.

1,000,000. The hundred-thousands digit is 2, so round down.

Write 0.125 as a fraction in simplest form.

1/8.

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