Calculating with decimals

For grown-ups: this lesson in words

Years 5 and 6 · Maths

Calculating with decimals: I can multiply and divide by 10, 100 and 1,000, and add, subtract, multiply and divide with decimals.

1. Here is 2.35 made with place value counters: 2 ones, 3 tenths and 5 hundredths.

   In 2.35, the decimal point sits after the 2 ones. The 3 tenths and 5 hundredths come after it.

   Picture: Place value counters showing 2.35: 2 ones, 3 tenths and 5 hundredths, with the number 2.35 written underneath, its decimal point after the 2.

2. 2.35 × 10 = 23.5

   Every digit moves one place to the left.

   Now the 2 is in the tens, the 3 is in the ones and the 5 is in the tenths.

   Multiplying by 10 moves every digit one place to the left.

   Picture: A place value chart showing 23.5: 2 tens, 3 ones and 5 tenths.

3. 36 ÷ 100 = 0.36

   Dividing moves the digits to the right. For 100, that is two places.

   Now the 3 is in the tenths and the 6 is in the hundredths. A 0 holds the ones place.

   Picture: A place value chart showing 0.36: 0 ones, 3 tenths and 6 hundredths.

4. 2.5 × 1,000 = 2,500

   For 1,000, move every digit three places to the left: one place for each zero in 1,000.

   The 2 is now in the thousands and the 5 is in the hundreds. Zeros hold the tens and ones places.

   Picture: A place value chart showing 2,500: 2 thousands, 5 hundreds, 0 tens and 0 ones.

5. Your turn: 4.7 × 10. Move every digit one place to the left. What is the answer?

   Picture: A place value chart showing 4.7: 4 ones and 7 tenths.

   Choose one:

   • 0.47
   • 4.70
   • 47

   Answer

   The answer: 47