Step-by-step Maths Level 5 Place value to a million and decimals to tenths: check-up and practice test questions

Method. Turn both numbers into tenths, then choose any tenths number between them.

1. Write both numbers in tenths. Count how many tenths each number has.
   3.7 = 37 tenths and 3.9 = 39 tenths
2. Find the tenths in between. Any number of tenths strictly between them works.
   3.8
3. Write an answer. Each is between the two numbers, so each is correct.
   Accept any of 3.8

Check. Check: each choice is greater than 3.7 and less than 3.9.

Watch out. Do not choose the same number as one of the two numbers in the question. It must be strictly between.

Method. Compare the numbers from the left, and write them smallest first.

1. Find the smallest number. Compare the digits from the left.
   Smallest: 145,974
2. Put the rest in order. Repeat: find the next smallest number.
   145,974 < 319,401 < 338,787 < 516,230
3. Write the list. Smallest first, as the question asks.
   145,974, 319,401, 338,787, 516,230

Check. Check: the first number is the smallest and the last is the largest.

Watch out. A number with more digits is greater; with the same number of digits, compare from the left.

Method. Read the thousands, then the last three digits, and join them with the word thousand.

1. Split the number into thousands and the last three digits. Read the thousands first, then the rest.
   537 thousand and 447
2. Say the thousands. Say the number before the thousand, then the word thousand.
   five hundred and thirty-seven thousand
3. Say the last three digits. Say them as a number up to 999.
   four hundred and forty-seven
4. Put the words together. Use a space between the two parts; use and before a number under 100.
   five hundred and thirty-seven thousand four hundred and forty-seven

Check. Check: count the words so that each part matches its digits.

Watch out. Do not write the digits in words one by one. Say the parts. Use and before the tens and ones.

Method. Read the column, then multiply the digit by the value of that column.

1. Find the thousands column. Count the columns from the right: ones, tens, hundreds and so on.
   The digit is 8
2. Multiply the digit by the value of its column. Each place in the thousands column is worth 1,000.
   8 × 1,000 = 8,000
3. Write the value. This is the value of the digit in this number, not just the digit.
   8,000

Check. Check: 8,000 is 8 groups of 1,000.

Watch out. Say the value, such as 70,000, not only the digit 7.

Method. Turn both numbers into tenths, then choose any tenths number between them.

1. Write both numbers in tenths. Count how many tenths each number has.
   1.4 = 14 tenths and 1.6 = 16 tenths
2. Find the tenths in between. Any number of tenths strictly between them works.
   1.5
3. Write an answer. Each is between the two numbers, so each is correct.
   Accept any of 1.5

Check. Check: each choice is greater than 1.4 and less than 1.6.

Watch out. Do not choose the same number as one of the two numbers in the question. It must be strictly between.

Method. Look at the digit to the right of the tens column, then decide.

1. Look at the ones digit. This digit decides whether to round up or down.
   The ones digit is 7
2. Decide: round up or down. 5 or more: round up. 4 or less: round down.
   7 is 5 or more, so round up
3. Write the rounded number. Replace the digits after the tens column with zeros.
   820,240

Check. Check: 820,240 is a multiple of 10 and is the closest one to 820,237.

Watch out. Round up only when the next digit is 5 or more. Do not round up on a 4.

Method. Partition the number into the value of each digit.

1. Find the value of each digit. Multiply each digit by the value of its column; leave out zeros.
   900,000, 20,000, 2,000, 80, 4
2. Write the parts as an addition. Add the parts together to make the number.
   900,000 + 20,000 + 2,000 + 80 + 4
3. Check by adding. Adding the parts again must give the number we started with.
   900,000 + 20,000 + 2,000 + 80 + 4

Check. Check: the parts add to 922,084.

Watch out. Leave out any digit that is zero. Zero adds nothing.

Method. Compare the whole numbers first, then the tenths.

1. Compare the whole numbers. Put the numbers with the smallest whole number first.
   5, 6, 5, 9
2. Compare the tenths when the whole numbers match. Use the tenths digit to break a tie.
   5.0, 6.8, 5.5, 9.3
3. Write the list smallest first. Read the order from the smallest to the largest.
   5.0, 5.5, 6.8, 9.3

Check. Check: the first number is the smallest and the last is the greatest.

Watch out. Do not order by the number of digits after the point. 4.2 is greater than 3.9.

Method. Compare the whole numbers, then the tenths.

1. Compare the whole numbers first. The bigger whole number is the bigger decimal.
   8 and 7
2. If the whole numbers are the same, compare the tenths. The tenths digit decides when the whole numbers match.
   0 and 4 tenths
3. Choose the greater decimal. This is the decimal with more of the bigger part.
   8.0

Check. Check: 8.0 is 80 tenths, and 7.4 is 74 tenths.

Watch out. 3.7 is greater than 3.4, not smaller. Compare the tenths: 7 tenths is more than 4 tenths.

Method. Look at the digit to the right of the thousands column, then decide.

1. Look at the hundreds digit. This digit decides whether to round up or down.
   The hundreds digit is 0
2. Decide: round up or down. 5 or more: round up. 4 or less: round down.
   0 is 4 or less, so round down
3. Write the rounded number. Replace the digits after the thousands column with zeros.
   285,000

Check. Check: 285,000 is a multiple of 1,000 and is the closest one to 285,067.

Watch out. Round up only when the next digit is 5 or more. Do not round up on a 4.

Method. Write the whole number, then a decimal point, then the tenths digit.

1. Write the whole number first. This is the part before the decimal point.
   8
2. Write the tenths after a decimal point. 5/10 is 5 tenths, so the digit 5 goes after the point.
   8.5
3. Write the answer. A decimal point separates the whole number from the tenths.
   8.5

Check. Check: 5/10 is 0.5, and 8 + 0.5 = 8.5.

Watch out. The tenths digit is one place after the decimal point.

Method. Look at the digit to the right of the tens column, then decide.

1. Look at the ones digit. This digit decides whether to round up or down.
   The ones digit is 3
2. Decide: round up or down. 5 or more: round up. 4 or less: round down.
   3 is 4 or less, so round down
3. Write the rounded number. Replace the digits after the tens column with zeros.
   664,610

Check. Check: 664,610 is a multiple of 10 and is the closest one to 664,613.

Watch out. Round up only when the next digit is 5 or more. Do not round up on a 4.

Method. Read the thousands, then the last three digits, and join them with the word thousand.

1. Split the number into thousands and the last three digits. Read the thousands first, then the rest.
   583 thousand and 904
2. Say the thousands. Say the number before the thousand, then the word thousand.
   five hundred and eighty-three thousand
3. Say the last three digits. Say them as a number up to 999.
   nine hundred and four
4. Put the words together. Use a space between the two parts; use and before a number under 100.
   five hundred and eighty-three thousand nine hundred and four

Check. Check: count the words so that each part matches its digits.

Watch out. Do not write the digits in words one by one. Say the parts. Use and before the tens and ones.

Method. Partition the number into the value of each digit.

1. Find the value of each digit. Multiply each digit by the value of its column; leave out zeros.
   600,000, 80,000, 2,000, 700, 10, 9
2. Write the parts as an addition. Add the parts together to make the number.
   600,000 + 80,000 + 2,000 + 700 + 10 + 9
3. Check by adding. Adding the parts again must give the number we started with.
   600,000 + 80,000 + 2,000 + 700 + 10 + 9

Check. Check: the parts add to 682,719.

Watch out. Leave out any digit that is zero. Zero adds nothing.

Method. Look at the digit to the right of the ten thousands column, then decide.

1. Look at the thousands digit. This digit decides whether to round up or down.
   The thousands digit is 5
2. Decide: round up or down. 5 or more: round up. 4 or less: round down.
   5 is 5 or more, so round up
3. Write the rounded number. Replace the digits after the ten thousands column with zeros.
   270,000

Check. Check: 270,000 is a multiple of 10,000 and is the closest one to 265,571.

Watch out. Round up only when the next digit is 5 or more. Do not round up on a 4.

Method. Partition the number into the value of each digit.

1. Find the value of each digit. Multiply each digit by the value of its column; leave out zeros.
   200,000, 30,000, 5,000, 300, 50, 8
2. Write the parts as an addition. Add the parts together to make the number.
   200,000 + 30,000 + 5,000 + 300 + 50 + 8
3. Check by adding. Adding the parts again must give the number we started with.
   200,000 + 30,000 + 5,000 + 300 + 50 + 8

Check. Check: the parts add to 235,358.

Watch out. Leave out any digit that is zero. Zero adds nothing.

Method. Look at the digit to the right of the thousands column, then decide.

1. Look at the hundreds digit. This digit decides whether to round up or down.
   The hundreds digit is 3
2. Decide: round up or down. 5 or more: round up. 4 or less: round down.
   3 is 4 or less, so round down
3. Write the rounded number. Replace the digits after the thousands column with zeros.
   282,000

Check. Check: 282,000 is a multiple of 1,000 and is the closest one to 282,376.

Watch out. Round up only when the next digit is 5 or more. Do not round up on a 4.

Method. Compare the digits from the left. The first column where they differ decides.

1. Compare the two numbers from the left. Look at the digits in the same column, starting with the largest.
   2 and 5 in the first column
2. Find the first column where they differ. That column decides which number is greater.
   In the hundred thousands column: 2 and 5
3. Choose the greater number. The number with the greater digit in that column is greater.
   567,810

Check. Check: the other number is 216,103, which is smaller.

Watch out. Do not compare the last digits first. Start from the left.

Method. Write the whole number, then a decimal point, then the tenths digit.

1. Write the whole number first. This is the part before the decimal point.
   2
2. Write the tenths after a decimal point. 9/10 is 9 tenths, so the digit 9 goes after the point.
   2.9
3. Write the answer. A decimal point separates the whole number from the tenths.
   2.9

Check. Check: 9/10 is 0.9, and 2 + 0.9 = 2.9.

Watch out. The tenths digit is one place after the decimal point.

Method. Partition the number into the value of each digit.

1. Find the value of each digit. Multiply each digit by the value of its column; leave out zeros.
   700,000, 60,000, 8,000, 800, 50, 5
2. Write the parts as an addition. Add the parts together to make the number.
   700,000 + 60,000 + 8,000 + 800 + 50 + 5
3. Check by adding. Adding the parts again must give the number we started with.
   700,000 + 60,000 + 8,000 + 800 + 50 + 5

Check. Check: the parts add to 768,855.

Watch out. Leave out any digit that is zero. Zero adds nothing.