Year 6: Multiplying and dividing by 10, 100 and 1000

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 1 place to the left. The decimal point does not move.

1. Count how many places the digits move. 10 is 1 zero, so each digit moves 1 place to the left.
   0.46 × 10
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   0.46 moves 1 place to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   4.6

Check. Undo it: 4.6 ÷ 10 gives 0.46 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 1 place to the left. The decimal point does not move.

1. Count how many places the digits move. 10 is 1 zero, so each digit moves 1 place to the left.
   3.5 × 10
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   3.5 moves 1 place to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   35

Check. Undo it: 35 ÷ 10 gives 3.5 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 1 place to the left. The decimal point does not move.

1. Count how many places the digits move. 10 is 1 zero, so each digit moves 1 place to the left.
   0.047 × 10
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   0.047 moves 1 place to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   0.47

Check. Undo it: 0.47 ÷ 10 gives 0.047 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 1 place to the left. The decimal point does not move.

1. Count how many places the digits move. 10 is 1 zero, so each digit moves 1 place to the left.
   12.25 × 10
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   12.25 moves 1 place to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   122.5

Check. Undo it: 122.5 ÷ 10 gives 12.25 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 2 places to the left. The decimal point does not move.

1. Count how many places the digits move. 100 is 2 zeros, so each digit moves 2 places to the left.
   0.47 × 100
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   0.47 moves 2 places to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   47

Check. Undo it: 47 ÷ 100 gives 0.47 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 2 places to the left. The decimal point does not move.

1. Count how many places the digits move. 100 is 2 zeros, so each digit moves 2 places to the left.
   3.56 × 100
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   3.56 moves 2 places to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   356

Check. Undo it: 356 ÷ 100 gives 3.56 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 2 places to the left. The decimal point does not move.

1. Count how many places the digits move. 100 is 2 zeros, so each digit moves 2 places to the left.
   0.085 × 100
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   0.085 moves 2 places to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   8.5

Check. Undo it: 8.5 ÷ 100 gives 0.085 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 2 places to the left. The decimal point does not move.

1. Count how many places the digits move. 100 is 2 zeros, so each digit moves 2 places to the left.
   1.2 × 100
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   1.2 moves 2 places to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   120

Check. Undo it: 120 ÷ 100 gives 1.2 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 3 places to the left. The decimal point does not move.

1. Count how many places the digits move. 1000 is 3 zeros, so each digit moves 3 places to the left.
   0.4 × 1000
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   0.4 moves 3 places to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   400

Check. Undo it: 400 ÷ 1000 gives 0.4 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 3 places to the left. The decimal point does not move.

1. Count how many places the digits move. 1000 is 3 zeros, so each digit moves 3 places to the left.
   0.067 × 1000
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   0.067 moves 3 places to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   67

Check. Undo it: 67 ÷ 1000 gives 0.067 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 3 places to the left. The decimal point does not move.

1. Count how many places the digits move. 1000 is 3 zeros, so each digit moves 3 places to the left.
   2.5 × 1000
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   2.5 moves 3 places to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   2500

Check. Undo it: 2500 ÷ 1000 gives 2.5 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 3 places to the left. The decimal point does not move.

1. Count how many places the digits move. 1000 is 3 zeros, so each digit moves 3 places to the left.
   1.275 × 1000
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   1.275 moves 3 places to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   1275

Check. Undo it: 1275 ÷ 1000 gives 1.275 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 1 place to the right. The decimal point does not move.

1. Count how many places the digits move. 10 is 1 zero, so each digit moves 1 place to the right.
   4.6 ÷ 10
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   4.6 moves 1 place to the right
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   0.46

Check. Undo it: 0.46 × 10 gives 4.6 again. ✓

Watch out. Dividing makes the number smaller, so the digits move to the right. Keep a zero in the ones place when the answer is less than 1.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 1 place to the right. The decimal point does not move.

1. Count how many places the digits move. 10 is 1 zero, so each digit moves 1 place to the right.
   35 ÷ 10
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   35 moves 1 place to the right
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   3.5

Check. Undo it: 3.5 × 10 gives 35 again. ✓

Watch out. Dividing makes the number smaller, so the digits move to the right. Keep a zero in the ones place when the answer is less than 1.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 1 place to the right. The decimal point does not move.

1. Count how many places the digits move. 10 is 1 zero, so each digit moves 1 place to the right.
   12.5 ÷ 10
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   12.5 moves 1 place to the right
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   1.25

Check. Undo it: 1.25 × 10 gives 12.5 again. ✓

Watch out. Dividing makes the number smaller, so the digits move to the right. Keep a zero in the ones place when the answer is less than 1.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 1 place to the right. The decimal point does not move.

1. Count how many places the digits move. 10 is 1 zero, so each digit moves 1 place to the right.
   0.8 ÷ 10
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   0.8 moves 1 place to the right
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   0.08

Check. Undo it: 0.08 × 10 gives 0.8 again. ✓

Watch out. Dividing makes the number smaller, so the digits move to the right. Keep a zero in the ones place when the answer is less than 1.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 2 places to the right. The decimal point does not move.

1. Count how many places the digits move. 100 is 2 zeros, so each digit moves 2 places to the right.
   47 ÷ 100
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   47 moves 2 places to the right
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   0.47

Check. Undo it: 0.47 × 100 gives 47 again. ✓

Watch out. Dividing makes the number smaller, so the digits move to the right. Keep a zero in the ones place when the answer is less than 1.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 2 places to the right. The decimal point does not move.

1. Count how many places the digits move. 100 is 2 zeros, so each digit moves 2 places to the right.
   356 ÷ 100
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   356 moves 2 places to the right
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   3.56

Check. Undo it: 3.56 × 100 gives 356 again. ✓

Watch out. Dividing makes the number smaller, so the digits move to the right. Keep a zero in the ones place when the answer is less than 1.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 2 places to the right. The decimal point does not move.

1. Count how many places the digits move. 100 is 2 zeros, so each digit moves 2 places to the right.
   8.5 ÷ 100
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   8.5 moves 2 places to the right
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   0.085

Check. Undo it: 0.085 × 100 gives 8.5 again. ✓

Watch out. Dividing makes the number smaller, so the digits move to the right. Keep a zero in the ones place when the answer is less than 1.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 2 places to the right. The decimal point does not move.

1. Count how many places the digits move. 100 is 2 zeros, so each digit moves 2 places to the right.
   9 ÷ 100
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   9 moves 2 places to the right
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   0.09

Check. Undo it: 0.09 × 100 gives 9 again. ✓

Watch out. Dividing makes the number smaller, so the digits move to the right. Keep a zero in the ones place when the answer is less than 1.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 3 places to the right. The decimal point does not move.

1. Count how many places the digits move. 1000 is 3 zeros, so each digit moves 3 places to the right.
   400 ÷ 1000
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   400 moves 3 places to the right
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   0.4

Check. Undo it: 0.4 × 1000 gives 400 again. ✓

Watch out. Dividing makes the number smaller, so the digits move to the right. Keep a zero in the ones place when the answer is less than 1.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 3 places to the right. The decimal point does not move.

1. Count how many places the digits move. 1000 is 3 zeros, so each digit moves 3 places to the right.
   67 ÷ 1000
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   67 moves 3 places to the right
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   0.067

Check. Undo it: 0.067 × 1000 gives 67 again. ✓

Watch out. Dividing makes the number smaller, so the digits move to the right. Keep a zero in the ones place when the answer is less than 1.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 3 places to the right. The decimal point does not move.

1. Count how many places the digits move. 1000 is 3 zeros, so each digit moves 3 places to the right.
   2500 ÷ 1000
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   2500 moves 3 places to the right
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   2.5

Check. Undo it: 2.5 × 1000 gives 2500 again. ✓

Watch out. Dividing makes the number smaller, so the digits move to the right. Keep a zero in the ones place when the answer is less than 1.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 3 places to the right. The decimal point does not move.

1. Count how many places the digits move. 1000 is 3 zeros, so each digit moves 3 places to the right.
   75 ÷ 1000
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   75 moves 3 places to the right
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   0.075

Check. Undo it: 0.075 × 1000 gives 75 again. ✓

Watch out. Dividing makes the number smaller, so the digits move to the right. Keep a zero in the ones place when the answer is less than 1.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 2 places to the right. The decimal point does not move.

1. Count how many places the digits move. 100 is 2 zeros, so each digit moves 2 places to the right.
   3.6 ÷ 100
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   3.6 moves 2 places to the right
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   0.036

Check. Undo it: 0.036 × 100 gives 3.6 again. ✓

Watch out. Dividing makes the number smaller, so the digits move to the right. Keep a zero in the ones place when the answer is less than 1.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 1 place to the right. The decimal point does not move.

1. Count how many places the digits move. 10 is 1 zero, so each digit moves 1 place to the right.
   4.25 ÷ 10
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   4.25 moves 1 place to the right
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   0.425

Check. Undo it: 0.425 × 10 gives 4.25 again. ✓

Watch out. Dividing makes the number smaller, so the digits move to the right. Keep a zero in the ones place when the answer is less than 1.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 2 places to the left. The decimal point does not move.

1. Count how many places the digits move. 100 is 2 zeros, so each digit moves 2 places to the left.
   7 × 100
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   7 moves 2 places to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   700

Check. Undo it: 700 ÷ 100 gives 7 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 3 places to the left. The decimal point does not move.

1. Count how many places the digits move. 1000 is 3 zeros, so each digit moves 3 places to the left.
   0.6 × 1000
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   0.6 moves 3 places to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   600

Check. Undo it: 600 ÷ 1000 gives 0.6 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.