Step-by-step Maths Level 5: Numbers to a million, and decimals to tenths

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

1. Find the hundred thousands column. Count the columns from the right: ones, tens, hundreds and so on.
   The digit is 1
2. Multiply the digit by the value of its column. Each place in the hundred thousands column is worth 100,000.
   1 × 100,000 = 100,000
3. Write the value. This is the value of the digit in this number, not just the digit.
   100,000

Check. Check: 100,000 is 1 groups of 100,000.

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

Method. Compare the whole numbers, then the tenths.

1. Compare the whole numbers first. The bigger whole number is the bigger decimal.
   9 and 3
2. If the whole numbers are the same, compare the tenths. The tenths digit decides when the whole numbers match.
   2 and 9 tenths
3. Choose the greater decimal. This is the decimal with more of the bigger part.
   9.2

Check. Check: 9.2 is 92 tenths, and 3.9 is 39 tenths.

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

Method. Only the ten thousands digit changes when we add or take away 10,000.

1. Look at the ten thousands digit. Adding or taking away 10,000 changes this digit by one.
   The ten thousands digit is 6
2. Change that digit by one. Carry or borrow if the digit goes past 9 or below 0.
   6 - 1 = 5
3. Write the answer. All the other digits stay the same.
   251,850

Check. Check: 251,850 add 10,000 gives back 261,850.

Watch out. Do not change the thousands digit. 10,000 is not 1,000.

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 6
2. Decide: round up or down. 5 or more: round up. 4 or less: round down.
   6 is 5 or more, so round up
3. Write the rounded number. Replace the digits after the thousands column with zeros.
   822,000

Check. Check: 822,000 is a multiple of 1,000 and is the closest one to 821,656.

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

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

1. Look at the ten thousands digit. This digit decides whether to round up or down.
   The ten thousands digit is 2
2. Decide: round up or down. 5 or more: round up. 4 or less: round down.
   2 is 4 or less, so round down
3. Write the rounded number. Replace the digits after the hundred thousands column with zeros.
   100,000

Check. Check: 100,000 is a multiple of 100,000 and is the closest one to 128,473.

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.
   5 and 5 in the first column
2. Find the first column where they differ. That column decides which number is greater.
   In the ten thousands column: 6 and 3
3. Choose the greater number. The number with the greater digit in that column is greater.
   561,644

Check. Check: the other number is 535,634, which is smaller.

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

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

1. Compare the whole numbers. Put the numbers with the smallest whole number first.
   4, 7, 8, 1
2. Compare the tenths when the whole numbers match. Use the tenths digit to break a tie.
   4.9, 7.1, 8.9, 1.1
3. Write the list smallest first. Read the order from the smallest to the largest.
   1.1, 4.9, 7.1, 8.9

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. The first digit after the point is the number of tenths.

1. Find the tenths digit. It is the first digit after the decimal point.
   The digit is 5
2. Write its value. 5 tenths is 5/10.
   5/10 = 0.5
3. Write the answer. The value of the digit is a decimal less than one.
   0.5

Check. Check: 0.5 + 4 = 4.5.

Watch out. Do not write the digit as a whole number. 4 in 3.4 is 0.4, not 4.

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

1. Compare the whole numbers. Put the numbers with the smallest whole number first.
   9, 6, 4, 6
2. Compare the tenths when the whole numbers match. Use the tenths digit to break a tie.
   9.6, 6.1, 4.5, 6.5
3. Write the list smallest first. Read the order from the smallest to the largest.
   4.5, 6.1, 6.5, 9.6

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. Only the ten thousands digit changes when we add or take away 10,000.

1. Look at the ten thousands digit. Adding or taking away 10,000 changes this digit by one.
   The ten thousands digit is 8
2. Change that digit by one. Carry or borrow if the digit goes past 9 or below 0.
   8 + 1 = 9
3. Write the answer. All the other digits stay the same.
   595,397

Check. Check: 595,397 take away 10,000 gives back 585,397.

Watch out. Do not change the thousands digit. 10,000 is not 1,000.

Method. Only the ten thousands digit changes when we add or take away 10,000.

1. Look at the ten thousands digit. Adding or taking away 10,000 changes this digit by one.
   The ten thousands digit is 6
2. Change that digit by one. Carry or borrow if the digit goes past 9 or below 0.
   6 + 1 = 7
3. Write the answer. All the other digits stay the same.
   572,618

Check. Check: 572,618 take away 10,000 gives back 562,618.

Watch out. Do not change the thousands digit. 10,000 is not 1,000.

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

1. Find the hundred thousands column. Count the columns from the right: ones, tens, hundreds and so on.
   The digit is 5
2. Multiply the digit by the value of its column. Each place in the hundred thousands column is worth 100,000.
   5 × 100,000 = 500,000
3. Write the value. This is the value of the digit in this number, not just the digit.
   500,000

Check. Check: 500,000 is 5 groups of 100,000.

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

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.
   300,000, 70,000, 500, 40, 3
2. Write the parts as an addition. Add the parts together to make the number.
   300,000 + 70,000 + 500 + 40 + 3
3. Check by adding. Adding the parts again must give the number we started with.
   300,000 + 70,000 + 500 + 40 + 3

Check. Check: the parts add to 370,543.

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 2
2. Decide: round up or down. 5 or more: round up. 4 or less: round down.
   2 is 4 or less, so round down
3. Write the rounded number. Replace the digits after the ten thousands column with zeros.
   900,000

Check. Check: 900,000 is a multiple of 10,000 and is the closest one to 902,770.

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

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 8
2. Decide: round up or down. 5 or more: round up. 4 or less: round down.
   8 is 5 or more, so round up
3. Write the rounded number. Replace the digits after the ten thousands column with zeros.
   160,000

Check. Check: 160,000 is a multiple of 10,000 and is the closest one to 158,297.

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

Method. The first digit after the point is the number of tenths.

1. Find the tenths digit. It is the first digit after the decimal point.
   The digit is 8
2. Write its value. 8 tenths is 8/10.
   8/10 = 0.8
3. Write the answer. The value of the digit is a decimal less than one.
   0.8

Check. Check: 0.8 + 9 = 9.8.

Watch out. Do not write the digit as a whole number. 4 in 3.4 is 0.4, not 4.