Year 5: Dividing by 10, 100 and 1,000

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 10 does. Each digit becomes 10 times smaller, so it moves 1 place to the right. The digits move. The decimal point does not.
   7 tens become 7 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   70 ÷ 10 = 7
3. Write the answer.
   70 ÷ 10 = 7

Check. Go back: 7 × 10 = 70 (the digits move 1 place to the left). ✓

Watch out. Taking off zeros works here because 70 ends in 1 zero. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 10 does. Each digit becomes 10 times smaller, so it moves 1 place to the right. The digits move. The decimal point does not.
   2 hundreds become 2 tens
   5 tens become 5 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   250 ÷ 10 = 25
3. Write the answer.
   250 ÷ 10 = 25

Check. Go back: 25 × 10 = 250 (the digits move 1 place to the left). ✓

Watch out. Taking off zeros works here because 250 ends in 1 zero. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 10 does. Each digit becomes 10 times smaller, so it moves 1 place to the right. The digits move. The decimal point does not.
   1 thousand becomes 1 hundred
   3 hundreds become 3 tens
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   1,300 ÷ 10 = 130
3. Write the answer.
   1,300 ÷ 10 = 130

Check. Go back: 130 × 10 = 1,300 (the digits move 1 place to the left). ✓

Watch out. Taking off zeros works here because 1,300 ends in 2 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 10 does. Each digit becomes 10 times smaller, so it moves 1 place to the right. The digits move. The decimal point does not.
   8 thousands become 8 hundreds
   6 tens become 6 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   8,060 ÷ 10 = 806
3. Write the answer.
   8,060 ÷ 10 = 806

Check. Go back: 806 × 10 = 8,060 (the digits move 1 place to the left). ✓

Watch out. Taking off zeros works here because 8,060 ends in 1 zero. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   8 hundreds become 8 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   800 ÷ 100 = 8
3. Write the answer.
   800 ÷ 100 = 8

Check. Go back: 8 × 100 = 800 (the digits move 2 places to the left). ✓

Watch out. Taking off zeros works here because 800 ends in 2 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   4 thousands become 4 tens
   5 hundreds become 5 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   4,500 ÷ 100 = 45
3. Write the answer.
   4,500 ÷ 100 = 45

Check. Go back: 45 × 100 = 4,500 (the digits move 2 places to the left). ✓

Watch out. Taking off zeros works here because 4,500 ends in 2 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   3 ten thousands become 3 hundreds
   6 thousands become 6 tens
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   36,000 ÷ 100 = 360
3. Write the answer.
   36,000 ÷ 100 = 360

Check. Go back: 360 × 100 = 36,000 (the digits move 2 places to the left). ✓

Watch out. Taking off zeros works here because 36,000 ends in 3 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   7 thousands become 7 tens
   3 hundreds become 3 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   7,300 ÷ 100 = 73
3. Write the answer.
   7,300 ÷ 100 = 73

Check. Go back: 73 × 100 = 7,300 (the digits move 2 places to the left). ✓

Watch out. Taking off zeros works here because 7,300 ends in 2 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   9 thousands become 9 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   9,000 ÷ 1,000 = 9
3. Write the answer.
   9,000 ÷ 1,000 = 9

Check. Go back: 9 × 1,000 = 9,000 (the digits move 3 places to the left). ✓

Watch out. Taking off zeros works here because 9,000 ends in 3 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   4 ten thousands become 4 tens
   2 thousands become 2 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   42,000 ÷ 1,000 = 42
3. Write the answer.
   42,000 ÷ 1,000 = 42

Check. Go back: 42 × 1,000 = 42,000 (the digits move 3 places to the left). ✓

Watch out. Taking off zeros works here because 42,000 ends in 3 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   6 thousands become 6 ones
   5 hundreds become 5 tenths
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   6,500 ÷ 1,000 = 6.5
3. Write the answer.
   6,500 ÷ 1,000 = 6.5

Check. Go back: 6.5 × 1,000 = 6,500 (the digits move 3 places to the left). ✓

Watch out. The answer has a decimal point because 6,500 does not end in enough zeros. The point goes between the ones and the tenths.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   7 hundreds become 7 tenths
   8 tens become 8 hundredths
2. Fill the empty places with zeros. The ones column is empty. A zero in it is a place holder: it keeps every digit in its right column.
   780 ÷ 1,000 = 0.78
3. Write the answer.
   780 ÷ 1,000 = 0.78

Check. Go back: 0.78 × 1,000 = 780 (the digits move 3 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.78, not .78.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 10 does. Each digit becomes 10 times smaller, so it moves 1 place to the right. The digits move. The decimal point does not.
   5 hundreds become 5 tens
   4 tens become 4 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   540 ÷ 10 = 54
3. Write the answer.
   540 ÷ 10 = 54

Check. Go back: 54 × 10 = 540 (the digits move 1 place to the left). ✓

Watch out. Taking off zeros works here because 540 ends in 1 zero. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   5 hundreds become 5 ones
   4 tens become 4 tenths
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   540 ÷ 100 = 5.4
3. Write the answer.
   540 ÷ 100 = 5.4

Check. Go back: 5.4 × 100 = 540 (the digits move 2 places to the left). ✓

Watch out. The answer has a decimal point because 540 does not end in enough zeros. The point goes between the ones and the tenths.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   5 hundreds become 5 tenths
   4 tens become 4 hundredths
2. Fill the empty places with zeros. The ones column is empty. A zero in it is a place holder: it keeps every digit in its right column.
   540 ÷ 1,000 = 0.54
3. Write the answer.
   540 ÷ 1,000 = 0.54

Check. Go back: 0.54 × 1,000 = 540 (the digits move 3 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.54, not .54.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 10 does. Each digit becomes 10 times smaller, so it moves 1 place to the right. The digits move. The decimal point does not.
   7 ones become 7 tenths
2. Fill the empty places with zeros. The ones column is empty. A zero in it is a place holder: it keeps every digit in its right column.
   7 ÷ 10 = 0.7
3. Write the answer.
   7 ÷ 10 = 0.7

Check. Go back: 0.7 × 10 = 7 (the digits move 1 place to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.7, not .7.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   2 thousands become 2 tens
   3 hundreds become 3 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   2,300 ÷ 100 = 23
3. Write the answer.
   2,300 ÷ 100 = 23

Check. Go back: 23 × 100 = 2,300 (the digits move 2 places to the left). ✓

Watch out. Taking off zeros works here because 2,300 ends in 2 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   9 tens become 9 tenths
   1 one becomes 1 hundredth
2. Fill the empty places with zeros. The ones column is empty. A zero in it is a place holder: it keeps every digit in its right column.
   91 ÷ 100 = 0.91
3. Write the answer.
   91 ÷ 100 = 0.91

Check. Go back: 0.91 × 100 = 91 (the digits move 2 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.91, not .91.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 10 does. Each digit becomes 10 times smaller, so it moves 1 place to the right. The digits move. The decimal point does not.
   3 ones become 3 tenths
   6 tenths become 6 hundredths
2. Move every digit 1 place to the right. Use a place-value chart and follow the arrows.
3. Fill the empty places with zeros. The ones column is empty. A zero in it is a place holder: it keeps every digit in its right column.
   3.6 ÷ 10 = 0.36
4. Write the answer.
   3.6 ÷ 10 = 0.36

Check. Go back: 0.36 × 10 = 3.6 (the digits move 1 place to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.36, not .36.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 10 does. Each digit becomes 10 times smaller, so it moves 1 place to the right. The digits move. The decimal point does not.
   7 tenths become 7 hundredths
2. Move every digit 1 place to the right. Use a place-value chart and follow the arrows.
3. Fill the empty places with zeros. The ones and tenths columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   0.7 ÷ 10 = 0.07
4. Write the answer.
   0.7 ÷ 10 = 0.07

Check. Go back: 0.07 × 10 = 0.7 (the digits move 1 place to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.07, not .07.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 10 does. Each digit becomes 10 times smaller, so it moves 1 place to the right. The digits move. The decimal point does not.
   1 ten becomes 1 one
   2 ones become 2 tenths
   4 tenths become 4 hundredths
2. Keep the decimal point between the ones and the tenths. The point stays still, so the digits that moved across it are now in the decimal columns.
   12.4 ÷ 10 = 1.24
3. Write the answer.
   12.4 ÷ 10 = 1.24

Check. Go back: 1.24 × 10 = 12.4 (the digits move 1 place to the left). ✓

Watch out. Dividing makes the number smaller. If your answer is bigger than 12.4, the digits moved the wrong way.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 10 does. Each digit becomes 10 times smaller, so it moves 1 place to the right. The digits move. The decimal point does not.
   5 hundredths become 5 thousandths
2. Fill the empty places with zeros. The ones and tenths and hundredths columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   0.05 ÷ 10 = 0.005
3. Write the answer.
   0.05 ÷ 10 = 0.005

Check. Go back: 0.005 × 10 = 0.05 (the digits move 1 place to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.005, not .005.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 10 does. Each digit becomes 10 times smaller, so it moves 1 place to the right. The digits move. The decimal point does not.
   8 ones become 8 tenths
   2 tenths become 2 hundredths
   5 hundredths become 5 thousandths
2. Fill the empty places with zeros. The ones column is empty. A zero in it is a place holder: it keeps every digit in its right column.
   8.25 ÷ 10 = 0.825
3. Write the answer.
   8.25 ÷ 10 = 0.825

Check. Go back: 0.825 × 10 = 8.25 (the digits move 1 place to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.825, not .825.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   2 ones become 2 hundredths
   4 tenths become 4 thousandths
2. Move every digit 2 places to the right. Use a place-value chart and follow the arrows.
3. Fill the empty places with zeros. The ones and tenths columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   2.4 ÷ 100 = 0.024
4. Write the answer.
   2.4 ÷ 100 = 0.024

Check. Go back: 0.024 × 100 = 2.4 (the digits move 2 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.024, not .024.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   3 tens become 3 tenths
   8 ones become 8 hundredths
2. Fill the empty places with zeros. The ones column is empty. A zero in it is a place holder: it keeps every digit in its right column.
   38 ÷ 100 = 0.38
3. Write the answer.
   38 ÷ 100 = 0.38

Check. Go back: 0.38 × 100 = 38 (the digits move 2 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.38, not .38.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   7 ones become 7 hundredths
   5 hundredths become 5 ten-thousandths
2. Fill the empty places with zeros. The ones and tenths columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   7.05 ÷ 100 = 0.0705
3. Write the answer.
   7.05 ÷ 100 = 0.0705

Check. Go back: 0.0705 × 100 = 7.05 (the digits move 2 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.0705, not .0705.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   9 ones become 9 thousandths
2. Fill the empty places with zeros. The ones and tenths and hundredths columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   9 ÷ 1,000 = 0.009
3. Write the answer.
   9 ÷ 1,000 = 0.009

Check. Go back: 0.009 × 1,000 = 9 (the digits move 3 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.009, not .009.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   3 hundreds become 3 tenths
   4 tens become 4 hundredths
   7 ones become 7 thousandths
   2 tenths become 2 ten-thousandths
2. Fill the empty places with zeros. The ones column is empty. A zero in it is a place holder: it keeps every digit in its right column.
   347.2 ÷ 1,000 = 0.3472
3. Write the answer.
   347.2 ÷ 1,000 = 0.3472

Check. Go back: 0.3472 × 1,000 = 347.2 (the digits move 3 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.3472, not .3472.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   6 tens become 6 hundredths
   2 ones become 2 thousandths
2. Fill the empty places with zeros. The ones and tenths columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   62 ÷ 1,000 = 0.062
3. Write the answer.
   62 ÷ 1,000 = 0.062

Check. Go back: 0.062 × 1,000 = 62 (the digits move 3 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.062, not .062.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. Find out how far the digits move. One place to the right is ÷ 10, two places is ÷ 100 and three places is ÷ 1,000.

1. Compare the two numbers. Look at how the digits have moved from the start number to the answer.
   4.5 → 0.045
2. Count how many places the digits moved. Each digit moved to the right, so the number got smaller.
3. Say what the number is. Digits that move 2 places to the right mean ÷ 100.
   4.5 ÷ 100 = 0.045

Check. 4.5 ÷ 100 = 0.045. ✓

Watch out. Put your answer back in the box and read the whole sentence. It must be true.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. Multiplying and dividing undo each other. Multiply the answer by 10 (move the digits 1 place to the left) to find the missing number.

1. Use the opposite (inverse) operation. Multiplying undoes dividing. The missing number is 3.6 × 10.
   3.6 × 10
2. Move the digits 1 place to the left. Multiplying by 10 makes each digit 10 times bigger.
3. Write the missing number. Read the whole sentence back to check it.
   36 ÷ 10 = 3.6

Check. 36 ÷ 10 = 3.6. ✓

Watch out. Put your answer back in the box and read the whole sentence. It must be true.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. Find out how far the digits move. One place to the right is ÷ 10, two places is ÷ 100 and three places is ÷ 1,000.

1. Compare the two numbers. Look at how the digits have moved from the start number to the answer.
   70 → 0.07
2. Count how many places the digits moved. Each digit moved to the right, so the number got smaller.
3. Say what the number is. Digits that move 3 places to the right mean ÷ 1,000.
   70 ÷ 1,000 = 0.07

Check. 70 ÷ 1,000 = 0.07. ✓

Watch out. Put your answer back in the box and read the whole sentence. It must be true.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. Multiplying and dividing undo each other. Multiply the answer by 100 (move the digits 2 places to the left) to find the missing number.

1. Use the opposite (inverse) operation. Multiplying undoes dividing. The missing number is 0.029 × 100.
   0.029 × 100
2. Move the digits 2 places to the left. Multiplying by 100 makes each digit 100 times bigger.
3. Write the missing number. Read the whole sentence back to check it.
   2.9 ÷ 100 = 0.029

Check. 2.9 ÷ 100 = 0.029. ✓

Watch out. Put your answer back in the box and read the whole sentence. It must be true.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. Find out how far the digits move. One place to the right is ÷ 10, two places is ÷ 100 and three places is ÷ 1,000.

1. Compare the two numbers. Look at how the digits have moved from the start number to the answer.
   63 → 6.3
2. Count how many places the digits moved. Each digit moved to the right, so the number got smaller.
3. Say what the number is. Digits that move 1 place to the right mean ÷ 10.
   63 ÷ 10 = 6.3

Check. 63 ÷ 10 = 6.3. ✓

Watch out. Put your answer back in the box and read the whole sentence. It must be true.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. Multiplying and dividing undo each other. Multiply the answer by 1,000 (move the digits 3 places to the left) to find the missing number.

1. Use the opposite (inverse) operation. Multiplying undoes dividing. The missing number is 0.804 × 1,000.
   0.804 × 1,000
2. Move the digits 3 places to the left. Multiplying by 1,000 makes each digit 1,000 times bigger.
3. Write the missing number. Read the whole sentence back to check it.
   804 ÷ 1,000 = 0.804

Check. 804 ÷ 1,000 = 0.804. ✓

Watch out. Put your answer back in the box and read the whole sentence. It must be true.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. Look at where each digit starts and where it ends. The number of places it moves tells you what you divided by.

1. Read the top number and the bottom number. The top row is the starting number. The bottom row is the answer.
   Top: 235.   Bottom: 2.35.
2. Look at the arrows. Every digit moves 2 places to the right. One place is ÷ 10, two places is ÷ 100, three places is ÷ 1,000.
   2 places to the right means ÷ 100.
3. Write the calculation.
   235 ÷ 100 = 2.35

Check. Move the digits of 235 2 places to the right: 2.35. ✓

Watch out. Arrows pointing right mean the number gets smaller, so it is a division.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. Look at where each digit starts and where it ends. The number of places it moves tells you what you divided by.

1. Read the top number and the bottom number. The top row is the starting number. The bottom row is the answer.
   Top: 18.   Bottom: 1.8.
2. Look at the arrows. Every digit moves 1 place to the right. One place is ÷ 10, two places is ÷ 100, three places is ÷ 1,000.
   1 place to the right means ÷ 10.
3. Write the calculation.
   18 ÷ 10 = 1.8

Check. Move the digits of 18 1 place to the right: 1.8. ✓

Watch out. Arrows pointing right mean the number gets smaller, so it is a division.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. Changing m into km makes the number smaller (the new unit is bigger), so divide by 1,000.

1. Decide what to do. 1 km = 1,000 m, so there are 1,000 times as many m as km. Dividing makes the number smaller.
   3,500 m ÷ 1,000
2. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   3 thousands become 3 ones
   5 hundreds become 5 tenths
3. Move every digit 3 places to the right. Use a place-value chart and follow the arrows.
4. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   3,500 ÷ 1,000 = 3.5
5. Write the answer with its unit.
   3.5 km

Check. Go back: 3.5 × 1,000 = 3,500 (the digits move 3 places to the left). ✓

Watch out. Check the units: a bigger unit means a smaller number. The km are the bigger unit.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. Changing cm into m makes the number smaller (the new unit is bigger), so divide by 100.

1. Decide what to do. 1 m = 100 cm, so there are 100 times as many cm as m. Dividing makes the number smaller.
   450 cm ÷ 100
2. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   4 hundreds become 4 ones
   5 tens become 5 tenths
3. Move every digit 2 places to the right. Use a place-value chart and follow the arrows.
4. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   450 ÷ 100 = 4.5
5. Write the answer with its unit.
   4.5 m

Check. Go back: 4.5 × 100 = 450 (the digits move 2 places to the left). ✓

Watch out. Check the units: a bigger unit means a smaller number. The m are the bigger unit.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. Changing g into kg makes the number smaller (the new unit is bigger), so divide by 1,000.

1. Decide what to do. 1 kg = 1,000 g, so there are 1,000 times as many g as kg. Dividing makes the number smaller.
   2,750 g ÷ 1,000
2. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   2 thousands become 2 ones
   7 hundreds become 7 tenths
   5 tens become 5 hundredths
3. Move every digit 3 places to the right. Use a place-value chart and follow the arrows.
4. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   2,750 ÷ 1,000 = 2.75
5. Write the answer with its unit.
   2.75 kg

Check. Go back: 2.75 × 1,000 = 2,750 (the digits move 3 places to the left). ✓

Watch out. Check the units: a bigger unit means a smaller number. The kg are the bigger unit.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. Changing ml into litres makes the number smaller (the new unit is bigger), so divide by 1,000.

1. Decide what to do. 1 litres = 1,000 ml, so there are 1,000 times as many ml as litres. Dividing makes the number smaller.
   825 ml ÷ 1,000
2. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   8 hundreds become 8 tenths
   2 tens become 2 hundredths
   5 ones become 5 thousandths
3. Move every digit 3 places to the right. Use a place-value chart and follow the arrows.
4. Fill the empty places with zeros. The ones column is empty. A zero in it is a place holder: it keeps every digit in its right column.
   825 ÷ 1,000 = 0.825
5. Write the answer with its unit.
   0.825 litres

Check. Go back: 0.825 × 1,000 = 825 (the digits move 3 places to the left). ✓

Watch out. Check the units: a bigger unit means a smaller number. The litres are the bigger unit.

Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.

Method. Changing pence into pounds makes the number smaller (the new unit is bigger), so divide by 100.

1. Decide what to do. £1 = 100p, so there are 100 times as many pence as pounds. Dividing makes the number smaller.
   365p ÷ 100
2. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   3 hundreds become 3 ones
   6 tens become 6 tenths
   5 ones become 5 hundredths
3. Move every digit 2 places to the right. Use a place-value chart and follow the arrows.
4. Keep the decimal point between the ones and the tenths. The point stays still, so the digits that moved across it are now in the decimal columns.
   365 ÷ 100 = 3.65
5. Write the answer with its unit.
   £3.65

Check. Go back: 3.65 × 100 = 365 (the digits move 2 places to the left). ✓

Watch out. Check the units: a bigger unit means a smaller number. The pounds are the bigger unit.

Key words. A counter-example is one example that shows a statement is false.

Method. Try some examples. If the statement is true for every example you can find, ask why. If you find one that is false, it cannot be “always”.

1. Try some numbers. Test the statement with some examples.
   300 ÷ 100 = 3 (the 3 moves 2 places to the right)
   45 ÷ 100 = 0.45 (the 4 and 5 both move 2 places)
   7.5 ÷ 100 = 0.075
2. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   Dividing by 100 makes every digit 100 times smaller. A digit that is 100 times smaller is two places to the right. This is true for whole numbers and for decimals.
3. Decide.
   Always

Check. In every example the digits moved two places to the right. ✓

Watch out. “Always” means every time. “Sometimes” needs one example that works and one that does not. “Never” means no example works.

Key words. A counter-example is one example that shows a statement is false.

Method. Try some examples. If the statement is true for every example you can find, ask why. If you find one that is false, it cannot be “always”.

1. Try some numbers. Test the statement with some examples.
   70 ÷ 10 = 7 (a whole number)
   75 ÷ 10 = 7.5 (not a whole number)
2. Look for one that does not work. One example that breaks the rule is called a counter-example.
   75 ÷ 10 = 7.5 is not a whole number.
3. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   If the number ends in 0, the digits move and the answer is a whole number. If it does not, a digit moves across the decimal point and the answer is a decimal.
4. Decide.
   Sometimes

Check. We found one example each way. ✓

Watch out. “Always” means every time. “Sometimes” needs one example that works and one that does not. “Never” means no example works.