Year 5: Multiplying 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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   7 ones become 7 tens
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 = 70
3. Write the answer.
   7 × 10 = 70

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

Watch out. The zeros are place holders. Check the answer is 10 times bigger: it has 1 more digit than 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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   4 tens become 4 hundreds
   6 ones become 6 tens
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.
   46 × 10 = 460
3. Write the answer.
   46 × 10 = 460

Check. Go back: 460 ÷ 10 = 46 (the digits move 1 place to the right). ✓

Watch out. The zeros are place holders. Check the answer is 10 times bigger: it has 1 more digit than 46.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   1 hundred becomes 1 thousand
   3 tens become 3 hundreds
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.
   130 × 10 = 1,300
3. Write the answer.
   130 × 10 = 1,300

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

Watch out. Count the zeros: 130 already ends in 1 zero, so the answer ends in 2 zeros.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   9 hundreds become 9 thousands
   5 ones become 5 tens
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.
   905 × 10 = 9,050
3. Write the answer.
   905 × 10 = 9,050

Check. Go back: 9,050 ÷ 10 = 905 (the digits move 1 place to the right). ✓

Watch out. The zeros are place holders. Check the answer is 10 times bigger: it has 1 more digit than 905.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   8 ones become 8 hundreds
2. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   8 × 100 = 800
3. Write the answer.
   8 × 100 = 800

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

Watch out. The zeros are place holders. Check the answer is 100 times bigger: it has 2 more digits than 8.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   5 tens become 5 thousands
   3 ones become 3 hundreds
2. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   53 × 100 = 5,300
3. Write the answer.
   53 × 100 = 5,300

Check. Go back: 5,300 ÷ 100 = 53 (the digits move 2 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 100 times bigger: it has 2 more digits than 53.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   4 hundreds become 4 ten thousands
   2 tens become 2 thousands
2. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   420 × 100 = 42,000
3. Write the answer.
   420 × 100 = 42,000

Check. Go back: 42,000 ÷ 100 = 420 (the digits move 2 places to the right). ✓

Watch out. Count the zeros: 420 already ends in 1 zero, so the answer ends in 3 zeros.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   3 hundreds become 3 ten thousands
   6 ones become 6 hundreds
2. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   306 × 100 = 30,600
3. Write the answer.
   306 × 100 = 30,600

Check. Go back: 30,600 ÷ 100 = 306 (the digits move 2 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 100 times bigger: it has 2 more digits than 306.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   9 ones become 9 thousands
2. Fill the empty places with zeros. The ones and tens and hundreds columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   9 × 1,000 = 9,000
3. Write the answer.
   9 × 1,000 = 9,000

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

Watch out. The zeros are place holders. Check the answer is 1,000 times bigger: it has 3 more digits than 9.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   6 tens become 6 ten thousands
   4 ones become 4 thousands
2. Fill the empty places with zeros. The ones and tens and hundreds columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   64 × 1,000 = 64,000
3. Write the answer.
   64 × 1,000 = 64,000

Check. Go back: 64,000 ÷ 1,000 = 64 (the digits move 3 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 1,000 times bigger: it has 3 more digits than 64.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   3 hundreds become 3 hundred thousands
   8 tens become 8 ten thousands
2. Fill the empty places with zeros. The ones and tens and hundreds columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   380 × 1,000 = 380,000
3. Write the answer.
   380 × 1,000 = 380,000

Check. Go back: 380,000 ÷ 1,000 = 380 (the digits move 3 places to the right). ✓

Watch out. Count the zeros: 380 already ends in 1 zero, so the answer ends in 4 zeros.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   7 hundreds become 7 hundred thousands
   4 tens become 4 ten thousands
   1 one becomes 1 thousand
2. Fill the empty places with zeros. The ones and tens and hundreds columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   741 × 1,000 = 741,000
3. Write the answer.
   741 × 1,000 = 741,000

Check. Go back: 741,000 ÷ 1,000 = 741 (the digits move 3 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 1,000 times bigger: it has 3 more digits than 741.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   6 tens become 6 hundreds
   2 ones become 2 tens
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.
   62 × 10 = 620
3. Write the answer.
   62 × 10 = 620

Check. Go back: 620 ÷ 10 = 62 (the digits move 1 place to the right). ✓

Watch out. The zeros are place holders. Check the answer is 10 times bigger: it has 1 more digit than 62.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   6 tens become 6 thousands
   2 ones become 2 hundreds
2. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   62 × 100 = 6,200
3. Write the answer.
   62 × 100 = 6,200

Check. Go back: 6,200 ÷ 100 = 62 (the digits move 2 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 100 times bigger: it has 2 more digits than 62.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   6 tens become 6 ten thousands
   2 ones become 2 thousands
2. Fill the empty places with zeros. The ones and tens and hundreds columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   62 × 1,000 = 62,000
3. Write the answer.
   62 × 1,000 = 62,000

Check. Go back: 62,000 ÷ 1,000 = 62 (the digits move 3 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 1,000 times bigger: it has 3 more digits than 62.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   3 hundreds become 3 thousands
   1 ten becomes 1 hundred
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.
   310 × 10 = 3,100
3. Write the answer.
   310 × 10 = 3,100

Check. Go back: 3,100 ÷ 10 = 310 (the digits move 1 place to the right). ✓

Watch out. Count the zeros: 310 already ends in 1 zero, so the answer ends in 2 zeros.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   2 hundreds become 2 ten thousands
   5 ones become 5 hundreds
2. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   205 × 100 = 20,500
3. Write the answer.
   205 × 100 = 20,500

Check. Go back: 20,500 ÷ 100 = 205 (the digits move 2 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 100 times bigger: it has 2 more digits than 205.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   4 tens become 4 ten thousands
   8 ones become 8 thousands
2. Fill the empty places with zeros. The ones and tens and hundreds columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   48 × 1,000 = 48,000
3. Write the answer.
   48 × 1,000 = 48,000

Check. Go back: 48,000 ÷ 1,000 = 48 (the digits move 3 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 1,000 times bigger: it has 3 more digits than 48.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   7 hundreds become 7 thousands
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.
   700 × 10 = 7,000
3. Write the answer.
   700 × 10 = 7,000

Check. Go back: 7,000 ÷ 10 = 700 (the digits move 1 place to the right). ✓

Watch out. Count the zeros: 700 already ends in 2 zeros, so the answer ends in 3 zeros.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   1 thousand becomes 1 hundred thousand
   5 hundreds become 5 ten thousands
2. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   1,500 × 100 = 150,000
3. Write the answer.
   1,500 × 100 = 150,000

Check. Go back: 150,000 ÷ 100 = 1,500 (the digits move 2 places to the right). ✓

Watch out. Count the zeros: 1,500 already ends in 2 zeros, so the answer ends in 4 zeros.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   3 ones become 3 tens
   6 tenths become 6 ones
2. Move every digit 1 place to the left. Use a place-value chart and follow the arrows.
3. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   3.6 × 10 = 36, not 36.0
4. Write the answer.
   3.6 × 10 = 36

Check. Go back: 36 ÷ 10 = 3.6 (the digits move 1 place to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (3.6 and 3.60 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   7 tenths become 7 ones
2. Move every digit 1 place to the left. Use a place-value chart and follow the arrows.
3. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   0.7 × 10 = 7, not 7.0
4. Write the answer.
   0.7 × 10 = 7

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

Watch out. Do not just add zeros to a decimal. That does not change its value (0.7 and 0.70 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   1 ten becomes 1 hundred
   2 ones become 2 tens
   4 tenths become 4 ones
2. Move every digit 1 place to the left. Use a place-value chart and follow the arrows.
3. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   12.4 × 10 = 124, not 124.0
4. Write the answer.
   12.4 × 10 = 124

Check. Go back: 124 ÷ 10 = 12.4 (the digits move 1 place to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (12.4 and 12.40 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   5 hundredths become 5 tenths
2. Move every digit 1 place to the left. Use a place-value chart and follow the arrows.
3. 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 whole-number columns.
   0.05 × 10 = 0.5
4. Write the answer.
   0.05 × 10 = 0.5

Check. Go back: 0.5 ÷ 10 = 0.05 (the digits move 1 place to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (0.05 and 0.050 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   8 ones become 8 tens
   2 tenths become 2 ones
   5 hundredths become 5 tenths
2. Move every digit 1 place to the left. Use a place-value chart and follow the arrows.
3. 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 whole-number columns.
   8.25 × 10 = 82.5
4. Write the answer.
   8.25 × 10 = 82.5

Check. Go back: 82.5 ÷ 10 = 8.25 (the digits move 1 place to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (8.25 and 8.250 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   2 ones become 2 hundreds
   4 tenths become 4 tens
2. Move every digit 2 places to the left. 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.
   2.4 × 100 = 240
4. Write the answer.
   2.4 × 100 = 240

Check. Go back: 240 ÷ 100 = 2.4 (the digits move 2 places to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (2.4 and 2.40 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   3 tenths become 3 tens
   8 hundredths become 8 ones
2. Move every digit 2 places to the left. Use a place-value chart and follow the arrows.
3. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   0.38 × 100 = 38, not 38.0
4. Write the answer.
   0.38 × 100 = 38

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

Watch out. Do not just add zeros to a decimal. That does not change its value (0.38 and 0.380 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   7 ones become 7 hundreds
   5 hundredths become 5 ones
2. Move every digit 2 places to the left. Use a place-value chart and follow the arrows.
3. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   7.05 × 100 = 705, not 705.0
4. Write the answer.
   7.05 × 100 = 705

Check. Go back: 705 ÷ 100 = 7.05 (the digits move 2 places to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (7.05 and 7.050 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   9 tenths become 9 hundreds
2. Move every digit 3 places to the left. Use a place-value chart and follow the arrows.
3. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   0.9 × 1,000 = 900
4. Write the answer.
   0.9 × 1,000 = 900

Check. Go back: 900 ÷ 1,000 = 0.9 (the digits move 3 places to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (0.9 and 0.90 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   3 ones become 3 thousands
   4 tenths become 4 hundreds
   7 hundredths become 7 tens
   2 thousandths become 2 ones
2. Move every digit 3 places to the left. Use a place-value chart and follow the arrows.
3. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   3.472 × 1,000 = 3,472, not 3,472.0
4. Write the answer.
   3.472 × 1,000 = 3,472

Check. Go back: 3,472 ÷ 1,000 = 3.472 (the digits move 3 places to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (3.472 and 3.4720 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   6 hundredths become 6 tens
   2 thousandths become 2 ones
2. Move every digit 3 places to the left. Use a place-value chart and follow the arrows.
3. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   0.062 × 1,000 = 62, not 62.0
4. Write the answer.
   0.062 × 1,000 = 62

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

Watch out. Do not just add zeros to a decimal. That does not change its value (0.062 and 0.0620 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Find out how far the digits move. One place to the left 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 → 450
2. Count how many places the digits moved. Each digit moved to the left, so the number got bigger.
3. Say what the number is. Digits that move 2 places to the left mean × 100.
   4.5 × 100 = 450

Check. 4.5 × 100 = 450. ✓

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

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

1. Use the opposite (inverse) operation. Dividing undoes multiplying. The missing number is 360 ÷ 10.
   360 ÷ 10
2. Move the digits 1 place to the right. Dividing by 10 makes each digit 10 times smaller.
3. Write the missing number. Read the whole sentence back to check it.
   36 × 10 = 360

Check. 36 × 10 = 360. ✓

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Find out how far the digits move. One place to the left 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.
   0.07 → 70
2. Count how many places the digits moved. Each digit moved to the left, so the number got bigger.
3. Say what the number is. Digits that move 3 places to the left mean × 1,000.
   0.07 × 1,000 = 70

Check. 0.07 × 1,000 = 70. ✓

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

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

1. Use the opposite (inverse) operation. Dividing undoes multiplying. The missing number is 290 ÷ 100.
   290 ÷ 100
2. Move the digits 2 places to the right. Dividing by 100 makes each digit 100 times smaller.
3. Write the missing number. Read the whole sentence back to check it.
   2.9 × 100 = 290

Check. 2.9 × 100 = 290. ✓

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Find out how far the digits move. One place to the left 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 → 630
2. Count how many places the digits moved. Each digit moved to the left, so the number got bigger.
3. Say what the number is. Digits that move 1 place to the left mean × 10.
   63 × 10 = 630

Check. 63 × 10 = 630. ✓

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

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

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

Check. 0.804 × 1,000 = 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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

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

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

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

Watch out. Arrows pointing left mean the number gets bigger, so it is a multiplication.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

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

1. Read the top number and the bottom number. The top row is the starting number. The bottom row is the answer.
   Top: 0.18.   Bottom: 1.8.
2. Look at the arrows. Every digit moves 1 place to the left. One place is × 10, two places is × 100, three places is × 1,000.
   1 place to the left means × 10.
3. Write the calculation.
   0.18 × 10 = 1.8

Check. Move the digits of 0.18 1 place to the left: 1.8. ✓

Watch out. Arrows pointing left mean the number gets bigger, so it is a multiplication.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Changing km into m makes the number bigger (there are more small units), so multiply by 1,000.

1. Decide what to do. 1 km = 1,000 m, so there are 1,000 times as many m as km. Multiply by 1,000.
   2.5 km × 1,000
2. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   2 ones become 2 thousands
   5 tenths become 5 hundreds
3. Move every digit 3 places to the left. Use a place-value chart and follow the arrows.
4. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   2.5 × 1,000 = 2,500
5. Write the answer with its unit.
   2,500 m

Check. Go back: 2,500 ÷ 1,000 = 2.5 (the digits move 3 places to the right). ✓

Watch out. Check the units: a smaller unit means a bigger number. The m are the smaller 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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Changing kg into g makes the number bigger (there are more small units), so multiply by 1,000.

1. Decide what to do. 1 kg = 1,000 g, so there are 1,000 times as many g as kg. Multiply by 1,000.
   3.7 kg × 1,000
2. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   3 ones become 3 thousands
   7 tenths become 7 hundreds
3. Move every digit 3 places to the left. Use a place-value chart and follow the arrows.
4. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   3.7 × 1,000 = 3,700
5. Write the answer with its unit.
   3,700 g

Check. Go back: 3,700 ÷ 1,000 = 3.7 (the digits move 3 places to the right). ✓

Watch out. Check the units: a smaller unit means a bigger number. The g are the smaller 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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Changing pounds into pence makes the number bigger (there are more small units), so multiply by 100.

1. Decide what to do. £1 = 100p, so there are 100 times as many pence as pounds. Multiply by 100.
   £4.85 × 100
2. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   4 ones become 4 hundreds
   8 tenths become 8 tens
   5 hundredths become 5 ones
3. Move every digit 2 places to the left. Use a place-value chart and follow the arrows.
4. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   4.85 × 100 = 485, not 485.0
5. Write the answer with its unit.
   485p

Check. Go back: 485 ÷ 100 = 4.85 (the digits move 2 places to the right). ✓

Watch out. Check the units: a smaller unit means a bigger number. The pence are the smaller 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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Changing litres into ml makes the number bigger (there are more small units), so multiply by 1,000.

1. Decide what to do. 1 litres = 1,000 ml, so there are 1,000 times as many ml as litres. Multiply by 1,000.
   0.6 litres × 1,000
2. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   6 tenths become 6 hundreds
3. Move every digit 3 places to the left. Use a place-value chart and follow the arrows.
4. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   0.6 × 1,000 = 600
5. Write the answer with its unit.
   600 ml

Check. Go back: 600 ÷ 1,000 = 0.6 (the digits move 3 places to the right). ✓

Watch out. Check the units: a smaller unit means a bigger number. The ml are the smaller 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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Changing m into cm makes the number bigger (there are more small units), so multiply by 100.

1. Decide what to do. 1 m = 100 cm, so there are 100 times as many cm as m. Multiply by 100.
   1.25 m × 100
2. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   1 one becomes 1 hundred
   2 tenths become 2 tens
   5 hundredths become 5 ones
3. Move every digit 2 places to the left. Use a place-value chart and follow the arrows.
4. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   1.25 × 100 = 125, not 125.0
5. Write the answer with its unit.
   125 cm

Check. Go back: 125 ÷ 100 = 1.25 (the digits move 2 places to the right). ✓

Watch out. Check the units: a smaller unit means a bigger number. The cm are the smaller 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.
   Move the digits 2 places left:
   3 × 100 = 300   0.4 × 100 = 40   12.5 × 100 = 1,250
2. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   Multiplying by 100 makes every digit 100 times bigger, which is always a move of 2 places to the left. This is true for whole numbers and for decimals.
3. Decide.
   Always

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

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.
   Whole numbers: 7 × 10 = 70   45 × 10 = 450 (ends in 0)
   Decimals: 0.5 × 10 = 5   3.2 × 10 = 32 (does not end in 0)
2. Look for one that does not work. One example that breaks the rule is called a counter-example.
   0.5 × 10 = 5, and 5 does not end in 0.
3. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   A whole number always gets a 0 place holder on the end. But a decimal can have digits move across the decimal point, so there might be no 0.
4. Decide.
   Sometimes

Check. Whole numbers always end in 0, but not every number is a whole number. ✓

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