Place Value and Rounding: practice solutions, Grade 4 – download the PDF

1 Value of each digit ★★★

Read each place from left to right.

• 5 is in the hundred thousands place: \(500{,}000\).
• 8 is in the ten thousands place: \(80{,}000\).
• 3 is in the thousands place: \(3{,}000\).
• 2 is in the hundreds place: \(200\).
• 1 is in the tens place: \(10\).
• 4 is in the ones place: \(4\).

Check: \(500{,}000 + 80{,}000 + 3{,}000 + 200 + 10 + 4 = 583{,}214\).

2 Video views ★★★

The digits are 7, 0, 5, 4, 2, 0 from left to right.

(a) The ten thousands place holds the digit 0.

(b) The 5 is in the thousands place, so it is worth \(5{,}000\).

(c) The 4 is in the hundreds place, so it is worth \(400\).

3 From words to digits ★★★

1. The thousands period is 460 and the ones period is 209: \(460{,}209\).
2. The thousands period is 81 and the ones period is 007 (we need placeholder zeros): \(81{,}007\).
3. The thousands period is 500 and the ones period is 030: \(500{,}030\).

4 From digits to words ★★★

1. seventy-two thousand, five hundred forty
2. three hundred five thousand, six
3. one million

Remember: no “and,” and a hyphen between the tens and ones words from 21 to 99.

5 Which symbol? ★★★

1. The numbers \(4{,}805\) and \(4{,}850\) match in the thousands and hundreds, then differ in the tens place, where 0 is less than 5. So \(4{,}805 \lt 4{,}850\).
2. \(67{,}210\) has five digits and \(9{,}999\) has four, so \(67{,}210 \gt 9{,}999\).
3. \(300{,}000 + 5{,}000 = 305{,}000\), so they are equal.
4. The numbers match in the ten thousands, thousands and hundreds places (1, 2 and 3). In the tens place, 4 is greater than 0, so \(12{,}340 \gt 12{,}304\).

6 Rounding to the nearest ten ★★★

1. The ones digit is 7, so round up: \(70\).
2. The ones digit is 4, so keep the tens: \(350\).
3. The ones digit is 6, so round up: \(2{,}400\).

7 Ten times as much ★★★

1. \(10 \times 90 = 900\).
2. \(10 \times 4{,}000 = 40{,}000\).
3. \(8{,}000 = 10 \times 800\), so the blank is \(800\).
4. \(50{,}000 = 10 \times 5{,}000\), so the blank is \(5{,}000\).

8 Comparing two digits ★★★

The three digits are in the hundred thousands, ten thousands and thousands places.

(a) The first 3 is worth \(300{,}000\) and the second 3 is worth \(30{,}000\). Since \(300{,}000 = 10 \times 30{,}000\), the answer is yes.

(b) The 5 is worth \(5{,}000\). Since \(30{,}000 \div 5{,}000 = 6\), the 3 is worth 6 times the 5, so the answer is no. The ten times rule compares the same digit in neighboring places.

9 Expanded form ★★★

1. \(538{,}206 = 500{,}000 + 30{,}000 + 8{,}000 + 200 + 6\).
2. \(70{,}090 = 70{,}000 + 90\) (the zeros are skipped).
3. The sum has no ten thousands and no hundreds, so those places are zeros: \(604{,}051\).

10 Putting numbers in order ★★★

All have five digits. The numbers starting with 83 are smaller than those starting with 85.

Among \(83{,}051\) and \(83{,}501\), the hundreds digit decides: 0 is less than 5. Among \(85{,}031\) and \(85{,}301\), the hundreds digit decides again: 0 is less than 3.

\(83{,}051 \lt 83{,}501 \lt 85{,}031 \lt 85{,}301\).

11 Stadium seats ★★★

The bars show A: \(38{,}000\), B: \(52{,}000\), C: \(27{,}000\), D: \(45{,}000\), E: \(61{,}000\).

(a) E (\(61{,}000\)) \(\gt\) B (\(52{,}000\)) \(\gt\) D (\(45{,}000\)) \(\gt\) A (\(38{,}000\)) \(\gt\) C (\(27{,}000\)).

(b) Look at the thousands digit. A: 8 rounds up to \(40{,}000\). B: 2 rounds down to \(50{,}000\). C: 7 rounds up to \(30{,}000\). D: 5 rounds up to \(50{,}000\). E: 1 rounds down to \(60{,}000\).

12 Rounding to the nearest hundred ★★★

Look at the tens digit each time.

1. The tens digit is 6: \(3{,}500\).
2. The tens digit is 5: round up to \(9{,}000\).
3. The tens digit is 4: stay at \(12{,}000\).
4. The tens digit is 5, so the 9 in the hundreds place goes up and carries over: \(100{,}000\).

13 Muffin sales ★★★

(a) The hundreds digit is 6, so round up: \(25{,}000\).

(b) The thousands digit is 4, so round down: \(20{,}000\).

(c) \(25{,}000 - 24{,}618 = 382\) and \(24{,}618 - 20{,}000 = 4{,}618\). The estimate \(25{,}000\) is much closer, because rounding to a smaller place keeps more detail.

14 A hiking estimate ★★★

(a) \(7{,}845 \approx 8{,}000\) and \(5{,}190 \approx 5{,}000\), so the total is about \(8{,}000 + 5{,}000 = 13{,}000\) feet.

(b) No. The exact total is \(7{,}845 + 5{,}190 = 13{,}035\) feet, so \(15{,}000\) is about \(2{,}000\) feet too high. The estimate \(13{,}000\) is much better.

15 Mystery number ★★★

Work one clue at a time.

• Hundred thousands: 7.
• Ten thousands: \(7 - 4 = 3\).
• Thousands: \(2 \times 3 = 6\).
• Hundreds: 0.
• Tens: \(3 + 6 = 9\).
• Ones: \(6 + 1 = 7\).

The mystery number is \(736{,}097\).

16 Greatest and least ★★★

(a) Put the greatest digits in the greatest places: 9, 7, 5, 4, 2, 0, giving \(975{,}420\).

(b) The first digit cannot be 0, so the smallest possible first digit is 2. Then use the rest from least to greatest: 0, 4, 5, 7, 9. The least number is \(204{,}579\).

17 All the numbers that round to 650,000 ★★★

Numbers round to \(650{,}000\) if they are closer to it than to \(640{,}000\) or \(660{,}000\). The midpoints are \(645{,}000\) and \(655{,}000\).

\(645{,}000\) rounds up to \(650{,}000\) because its thousands digit is 5. \(654{,}999\) rounds down to \(650{,}000\) because its thousands digit is 4, but \(655{,}000\) rounds up to \(660{,}000\).

The least is \(645{,}000\) and the greatest is \(654{,}999\).

18 Find the mistake ★★★

Maya looked at the hundreds digit, but the rule says to look at the digit to the right of the rounding place. For the nearest hundred, that digit is the tens digit, which is 9.

Since 9 is 5 or more, the hundreds digit 5 goes up to 6, and the rest becomes zeros. The correct answer is \(3{,}600\).

19 True or false? ★★★

1. True. \(10 \times 6{,}000 = 60{,}000\).
2. False. \(10 \times 9 = 90\). Since \(900 = 100 \times 9\), it is 100 times as much.
3. True. In \(4{,}500\) the hundreds digit is 5, so round up. In \(4{,}499\) the hundreds digit is 4, so round down.
4. False. The hundreds digit is 2, so the thousands digit stays: \(38{,}000\).

20 Rounding to the nearest hundred thousand ★★★

Look at the ten thousands digit.

• \(449{,}999\): the digit is 4, so \(400{,}000\).
• \(450{,}000\): the digit is 5, so \(500{,}000\).
• \(512{,}300\): the digit is 1, so \(500{,}000\).
• \(549{,}999\): the digit is 4, so \(500{,}000\).

The numbers \(449{,}999\) and \(450{,}000\) differ by 1 but round to \(400{,}000\) and \(500{,}000\). That is because \(450{,}000\) is exactly the midpoint, and the midpoint rounds up.

21 Tickets and precision ★★★

(a) \(19{,}000 + 21{,}000 + 19{,}000 = 59{,}000\).

(b) \(20{,}000 + 20{,}000 + 20{,}000 = 60{,}000\).

(c) The exact total is \(18{,}740 + 21{,}380 + 19{,}260 = 59{,}380\). It is less than \(60{,}000\), so the answer is no.

The estimate to the nearest thousand (\(59{,}000\)) was more helpful, because the rougher estimate of \(60{,}000\) hid the fact that the total is below \(60{,}000\).