- Identify the place value of the digit \(9\). - Identify the value of the first digit \(5\). - Match each nonzero digit to its expanded-form value.

1. The digit \(5\) in \(509{,}014\) has a value of \(500{,}000\). 2. The digit \(9\) has a value of \(9000\), the digit \(1\) has a value of \(10\), and the digit \(4\) has a value of \(4\). 3. Therefore, \(509{,}014 = 500{,}000 + 9000 + 10 + 4\), which is choice d).

d) \(500{,}000 + 9000 + 10 + 4\)

- Read each nonzero digit by its place value. - Expanded form writes the value contributed by each nonzero digit as a separate term.

1. The nonzero digits represent \(6\) ten-thousands, \(2\) thousands, \(4\) hundreds, and \(5\) ones. 2. Write one term for each nonzero place value: \(60{,}000+2000+400+5\).

\(60{,}000+2000+400+5\)

- Match each addend to the place value it represents. - If a place value has no term, its digit in standard form is zero.

1. Place each term in its matching place-value position. 2. The hundred-thousands digit is \(3\), the ten-thousands digit is \(4\), the hundreds digit is \(7\), the tens digit is \(2\), and the ones digit is \(6\). 3. The thousands place has no term, so its digit is \(0\). The standard form is \(340{,}726\).

\(340{,}726\)

- Identify the place value of the \(8\) and the \(3\) in the standard form. - Check each option by asking whether every term has the correct place value.

1. In \(508{,}030\), the \(8\) is in the thousands place and the \(3\) is in the tens place. 2. Therefore the nonzero place values are \(500{,}000\), \(8000\), and \(30\). 3. Choice A matches those values.

A) \(500{,}000+8000+30\)

- Each chip is worth the number at the top of its column. - Turn every nonempty column into one term. - Empty columns do not need separate zero terms in this expanded form.

1. Read the columns: \(4\) thousands, \(2\) hundreds, \(0\) tens, and \(5\) ones. 2. Add the nonzero values: \(4000+200+5\).

\(4000+200+5\).

- Identify the value of each nonzero digit. - Write one addend for each nonzero place. - A zero digit does not need its own addend.

1. a) \(49=40+9\). 2. b) \(166=100+60+6\). 3. c) \(944=900+40+4\). 4. d) \(2024=2000+20+4\). The zero in the hundreds place means there is no hundreds term.

a) \(40+9\) b) \(100+60+6\) c) \(900+40+4\) d) \(2000+20+4\)

- Match each addend with its place value. - Combine the thousands, hundreds, tens, and ones. - Check that every addend appears in the standard number.

1. a) \(70+4=74\). 2. b) \(400+40+4=444\). 3. c) \(900+90+9=999\). 4. d) \(1000+800+80+8=1888\).

a) \(74\) b) \(444\) c) \(999\) d) \(1888\)

- Find the value represented in each nonempty place-value column. - Multiply each chip count by the value of its column. - A place with no chips does not need a term in the expanded form.

1. The chart shows \(6\) chips in the ten-thousands column, \(2\) in the thousands column, \(8\) in the hundreds column, \(0\) in the tens column, and \(4\) in the ones column. 2. The nonzero place values are \(60{,}000\), \(2000\), \(800\), and \(4\). 3. The expanded form is \(60{,}000+2000+800+4\).

\(60{,}000+2000+800+4\)

- Read the chart one place-value column at a time from left to right. - In expanded form, include the value of each nonzero column. - Empty columns become zero digits in standard form and need no term in the expanded form.

1. The chart shows \(2\) hundred-thousands, \(0\) ten-thousands, \(4\) thousands, \(3\) hundreds, \(0\) tens, and \(6\) ones. 2. The expanded form is \(200{,}000+4000+300+6\). 3. The standard form is \(204{,}306\).

Expanded form: \(200{,}000+4000+300+6\) Standard form: \(204{,}306\)

- Read each nonzero digit from left to right and name its place. - Each digit has a value that depends on its place. - Use one addition term for each nonzero digit in expanded form.

1. The \(7\) is in the hundred-thousands place and has value \(700{,}000\). 2. The \(3\) is in the ten-thousands place and has value \(30{,}000\). 3. The \(4\) is in the thousands place and has value \(4000\). 4. The \(5\) is in the tens place and has value \(50\). 5. The \(2\) is in the ones place and has value \(2\). 6. The expanded form is \(700{,}000+30{,}000+4000+50+2\).

\(7\): hundred-thousands, \(700{,}000\) \(3\): ten-thousands, \(30{,}000\) \(4\): thousands, \(4000\) \(5\): tens, \(50\) \(2\): ones, \(2\) Expanded form: \(700{,}000+30{,}000+4000+50+2\)

- Locate every nonzero digit before writing any terms. - Ask what value a zero digit contributes to the number. - Expanded form does not need addends whose value is zero.

1. The nonzero digits are \(9\) hundred-thousands, \(5\) thousands, and \(7\) tens. 2. The expanded form is \(900{,}000+5000+70\). 3. The ten-thousands, hundreds, and ones digits are zero, so those places contribute no value and need no separate terms.

\(900{,}000+5000+70\). The omitted places have digit \(0\), so they contribute no value.

- Build the standard numeral one place at a time from the expanded terms. - Insert zero digits for place values that have no term. - Read the thousands period first, then the ones period.

1. Place the values into their positions: \(6\) hundred-thousands, \(2\) ten-thousands, \(9\) hundreds, and \(8\) ones. 2. The missing thousands and tens places are zeros, so the standard form is \(620{,}908\). 3. In words, the number is “six hundred twenty thousand nine hundred eight.”

Standard form: \(620{,}908\) Word form: six hundred twenty thousand nine hundred eight

- Identify which digits are nonzero and what each one is worth. - Write one expanded-form term for each nonzero place value. - For the word form, read the thousands period and then the remaining part of the number.

1. The nonzero place values are \(4\) hundred-thousands, \(3\) ten-thousands, and \(8\) tens. 2. The expanded form is \(400{,}000+30{,}000+80\). 3. In words, the number is “four hundred thirty thousand eighty.”

Expanded form: \(400{,}000+30{,}000+80\) Word form: four hundred thirty thousand eighty

- Identify the part of the number already shown by the first and last terms. - Which nonzero place value is still missing? - Check that your terms add to the original number.

1. The number has \(6\) ten-thousands, \(4\) hundreds, and \(7\) ones. 2. The missing term is \(400\), which represents the hundreds place.

\(400\); the hundreds place.

- Compare every term with the labeled column holding those chips. - A chip's value depends on its position in the chart. - Write one term for each nonempty place, then compare it with the student's expression.

1. The chart shows \(3\) thousands, no hundreds, \(5\) tens, and \(2\) ones. 2. The student read \(5\) tens as \(5\) hundreds and \(2\) ones as \(2\) tens. 3. The correct expanded form is \(3000+50+2\), worth \(3052\).

The \(5\) is in the tens column, and the \(2\) is in the ones column. Correct expanded form: \(3000+50+2\).

- For part b, write only the nonzero place-value parts. - In part c, remember that \(10\) hundreds can be regrouped as \(1\) thousand. - Add the place-value amounts to check each standard-form number.

1. For a), \(60{,}000 + 400 + 30 + 8 = 60{,}438\). 2. For b), the nonzero place values are \(300{,}000\), \(5000\), and \(70\), so \(305{,}070 = 300{,}000 + 5000 + 70\). 3. For c), \(12\) thousands is \(12{,}000\), \(15\) hundreds is \(1500\), and \(3\) ones is \(3\). Their sum is \(12{,}000 + 1500 + 3 = 13{,}503\).

a) \(60{,}438\) b) \(300{,}000 + 5000 + 70\) c) \(13{,}503\)

- Write the value represented by each column. - Only the tens term changes when two chips are removed from the tens column.

1. The chart shows \(8\) chips in the ten-thousands column, \(1\) in the thousands column, \(4\) in the hundreds column, \(5\) in the tens column, and \(6\) in the ones column. 2. Its expanded form is \(80{,}000 + 1000 + 400 + 50 + 6 = 81{,}456\). 3. Removing two tens chips changes \(5\) tens to \(3\) tens, so the tens term becomes \(30\). 4. The new expanded form is \(80{,}000 + 1000 + 400 + 30 + 6 = 81{,}436\).

Original: \(80{,}000 + 1000 + 400 + 50 + 6 = 81{,}456\) New: \(80{,}000 + 1000 + 400 + 30 + 6 = 81{,}436\)

- Compare each term Jordan wrote with the column that contains the corresponding chips. - Focus on the column containing \(2\) chips. - After correcting the expansion, read all six place-value columns to form the standard numeral.

1. The chart has \(2\) chips in the ten-thousands column, not the thousands column. 2. Jordan therefore used \(2000\) where the term should represent \(2\) ten-thousands. 3. The correct expanded form is \(400{,}000+20{,}000+600+30\). 4. The standard form is \(420{,}630\).

Jordan treated the \(2\) as thousands instead of ten-thousands. Correct expanded form: \(400{,}000+20{,}000+600+30\) Standard form: \(420{,}630\)

- Check whether any addend contains more than one place value. - Separate the thousands and hundreds in the middle addend. - Make sure the rewritten sum contains one term for each nonzero digit.

1. Break \(1200\) into \(1000+200\). 2. Combine the place values to get \(531{,}248\). 3. Write one term for each nonzero digit: \(500{,}000+30{,}000+1000+200+40+8\).

Standard form: \(531{,}248\) Expanded form: \(500{,}000+30{,}000+1000+200+40+8\)

- Look for amounts you can combine within each sum. - Check both sums before comparing them. - In expanded form, each nonzero digit gets its own place-value term.

1. Riley has \(30{,}000+10{,}000=40{,}000\), so the sum is \(240{,}600\). 2. Devon has \(100{,}000+100{,}000=200{,}000\) and \(500+100=600\), so Devon's sum is also \(240{,}600\). 3. The standard form is \(240{,}600\). The expanded form is \(200{,}000+40{,}000+600\).

Yes. Both sums equal \(240{,}600\). Standard form: \(240{,}600\). Expanded form: \(200{,}000+40{,}000+600\).

- Combine terms before reading the digit in each place. - Write the standard numeral before preparing its usual expanded form. - In word form, read the thousands group first and then the remaining places.

1. Combine the two contributions to the thousands: \(70{,}000+15{,}000=85{,}000\). 2. The number is \(485{,}896\). 3. Its usual expanded form is \(400{,}000+80{,}000+5000+800+90+6\). 4. The word form is four hundred eighty-five thousand eight hundred ninety-six. 5. The ten-thousands digit is \(8\).

a) \(485{,}896\) b) \(400{,}000+80{,}000+5000+800+90+6\) c) four hundred eighty-five thousand eight hundred ninety-six d) \(8\)