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Read large numbers, say what each digit is worth, and round to any place.
Question 1 of 12
Round 79,846 to the nearest 100.
Rounding to the nearest 100 means choosing between 79,800 and 79,900, because 79,846 sits between them. The digit that decides is the one in the tens place, and here that part is 46. Half of 100 is 50, and 46 is less than that, so it rounds down. The answer is 79,800. Underlining the digit being rounded, and circling the one that decides, stops most mistakes here.
The answer is B. Rounding to the nearest 100 means choosing between 79,800 and 79,900, because 79,846 sits between them. The digit that decides is the one in the tens place, and here that part is 46. Half of 100 is 50, and 46 is less than that, so it rounds down. The answer is 79,800. Underlining the digit being rounded, and circling the one that decides, stops most mistakes here.
Round 3,433,152 to the nearest 10,000.
Rounding to the nearest 10,000 means choosing between 3,430,000 and 3,440,000, because 3,433,152 sits between them. The digit that decides is the one in the thousands place, and here that part is 3,152. Half of 10,000 is 5,000, and 3,152 is less than that, so it rounds down. The answer is 3,430,000. Five rounds up. It is a convention rather than a rule of nature, but every mark scheme uses it.
The answer is C. Rounding to the nearest 10,000 means choosing between 3,430,000 and 3,440,000, because 3,433,152 sits between them. The digit that decides is the one in the thousands place, and here that part is 3,152. Half of 10,000 is 5,000, and 3,152 is less than that, so it rounds down. The answer is 3,430,000. Five rounds up. It is a convention rather than a rule of nature, but every mark scheme uses it.
In the number 4,797,995, what is the value of the digit 9 that is in the tens column?
The question asks for the value of the digit, not the digit itself. That 9 is sitting in the tens column, so it is worth 9 lots of 10, which is 90. Saying "9" would be answering a different question. Reading the number aloud in full — 4,797,995 — makes the column obvious, because you say the column name as you reach it. The trap is answering with the digit. The question is always worth a second read.
The answer is B. The question asks for the value of the digit, not the digit itself. That 9 is sitting in the tens column, so it is worth 9 lots of 10, which is 90. Saying "9" would be answering a different question. Reading the number aloud in full — 4,797,995 — makes the column obvious, because you say the column name as you reach it. The trap is answering with the digit. The question is always worth a second read.
Which of these numbers is the smallest?
All five numbers have the same amount of digits, so comparing them digit by digit from the left is the quickest way. They all begin 34 ten-thousands, so that column settles nothing; the thousands column is where they start to differ. 340,979 is the smallest. Line the numbers up under each other if they are close, and the difference jumps out.
The answer is B. All five numbers have the same amount of digits, so comparing them digit by digit from the left is the quickest way. They all begin 34 ten-thousands, so that column settles nothing; the thousands column is where they start to differ. 340,979 is the smallest. Line the numbers up under each other if they are close, and the difference jumps out.
In the number 5,729,355, what is the value of the digit 5 that is in the millions column?
The question asks for the value of the digit, not the digit itself. That 5 is sitting in the millions column, so it is worth 5 lots of 1,000,000, which is 5,000,000. Saying "5" would be answering a different question. Reading the number aloud in full — 5,729,355 — makes the column obvious, because you say the column name as you reach it. Writing the column headings above the number, once, settles every question of this kind.
The answer is A. The question asks for the value of the digit, not the digit itself. That 5 is sitting in the millions column, so it is worth 5 lots of 1,000,000, which is 5,000,000. Saying "5" would be answering a different question. Reading the number aloud in full — 5,729,355 — makes the column obvious, because you say the column name as you reach it. Writing the column headings above the number, once, settles every question of this kind.
In the number 5,356,223, what is the value of the digit 5 that is in the ten thousands column?
The question asks for the value of the digit, not the digit itself. That 5 is sitting in the ten thousands column, so it is worth 5 lots of 10,000, which is 50,000. Saying "5" would be answering a different question. Reading the number aloud in full — 5,356,223 — makes the column obvious, because you say the column name as you reach it. Writing the column headings above the number, once, settles every question of this kind.
The answer is C. The question asks for the value of the digit, not the digit itself. That 5 is sitting in the ten thousands column, so it is worth 5 lots of 10,000, which is 50,000. Saying "5" would be answering a different question. Reading the number aloud in full — 5,356,223 — makes the column obvious, because you say the column name as you reach it. Writing the column headings above the number, once, settles every question of this kind.
In the number 8,774,149, what is the value of the digit 7 that is in the ten thousands column?
The question asks for the value of the digit, not the digit itself. That 7 is sitting in the ten thousands column, so it is worth 7 lots of 10,000, which is 70,000. Saying "7" would be answering a different question. Reading the number aloud in full — 8,774,149 — makes the column obvious, because you say the column name as you reach it. The trap is answering with the digit. The question is always worth a second read.
The answer is B. The question asks for the value of the digit, not the digit itself. That 7 is sitting in the ten thousands column, so it is worth 7 lots of 10,000, which is 70,000. Saying "7" would be answering a different question. Reading the number aloud in full — 8,774,149 — makes the column obvious, because you say the column name as you reach it. The trap is answering with the digit. The question is always worth a second read.
In the number 2,281,727, what is the value of the digit 2 that is in the hundred thousands column?
The question asks for the value of the digit, not the digit itself. That 2 is sitting in the hundred thousands column, so it is worth 2 lots of 100,000, which is 200,000. Saying "2" would be answering a different question. Reading the number aloud in full — 2,281,727 — makes the column obvious, because you say the column name as you reach it. Writing the column headings above the number, once, settles every question of this kind.
The answer is B. The question asks for the value of the digit, not the digit itself. That 2 is sitting in the hundred thousands column, so it is worth 2 lots of 100,000, which is 200,000. Saying "2" would be answering a different question. Reading the number aloud in full — 2,281,727 — makes the column obvious, because you say the column name as you reach it. Writing the column headings above the number, once, settles every question of this kind.
Round 348,167 to the nearest 1,000.
Rounding to the nearest 1,000 means choosing between 348,000 and 349,000, because 348,167 sits between them. The digit that decides is the one in the hundreds place, and here that part is 167. Half of 1,000 is 500, and 167 is less than that, so it rounds down. The answer is 348,000. Five rounds up. It is a convention rather than a rule of nature, but every mark scheme uses it.
The answer is A. Rounding to the nearest 1,000 means choosing between 348,000 and 349,000, because 348,167 sits between them. The digit that decides is the one in the hundreds place, and here that part is 167. Half of 1,000 is 500, and 167 is less than that, so it rounds down. The answer is 348,000. Five rounds up. It is a convention rather than a rule of nature, but every mark scheme uses it.
All five numbers have the same amount of digits, so comparing them digit by digit from the left is the quickest way. They all begin 64 ten-thousands, so that column settles nothing; the thousands column is where they start to differ. 640,653 is the smallest. Line the numbers up under each other if they are close, and the difference jumps out.
The answer is B. All five numbers have the same amount of digits, so comparing them digit by digit from the left is the quickest way. They all begin 64 ten-thousands, so that column settles nothing; the thousands column is where they start to differ. 640,653 is the smallest. Line the numbers up under each other if they are close, and the difference jumps out.
In the number 3,946,797, what is the value of the digit 9 that is in the tens column?
The question asks for the value of the digit, not the digit itself. That 9 is sitting in the tens column, so it is worth 9 lots of 10, which is 90. Saying "9" would be answering a different question. Reading the number aloud in full — 3,946,797 — makes the column obvious, because you say the column name as you reach it. Each step left is ten times bigger. That single fact is the whole of place value.
The answer is D. The question asks for the value of the digit, not the digit itself. That 9 is sitting in the tens column, so it is worth 9 lots of 10, which is 90. Saying "9" would be answering a different question. Reading the number aloud in full — 3,946,797 — makes the column obvious, because you say the column name as you reach it. Each step left is ten times bigger. That single fact is the whole of place value.
Round 719,129 to the nearest 1,000.
Rounding to the nearest 1,000 means choosing between 719,000 and 720,000, because 719,129 sits between them. The digit that decides is the one in the hundreds place, and here that part is 129. Half of 1,000 is 500, and 129 is less than that, so it rounds down. The answer is 719,000. The digit to look at is the one immediately to the right of the place you are rounding to. Everything after it is a distraction.
The answer is D. Rounding to the nearest 1,000 means choosing between 719,000 and 720,000, because 719,129 sits between them. The digit that decides is the one in the hundreds place, and here that part is 129. Half of 1,000 is 500, and 129 is less than that, so it rounds down. The answer is 719,000. The digit to look at is the one immediately to the right of the place you are rounding to. Everything after it is a distraction.
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