Moving the decimal point: multiplying by 10, 100 and 1,000
Discover Mathematics P5: Term 1, Unit 5, Lessons 1–4
GoalMultiply a decimal by 10, 100 and 1,000 by moving the digits, and use it in stories and metric units.
New words
decimal point · the dot between the ones place and the tenths placepower of ten · 10, 100, 1,000 and so onconvert · to change a measure into another unit, such as metres into centimetres
Explanation
When we multiply a decimal by 10, 100 or 1,000, every digit moves to the left: one place for 10, two places for 100 and three places for 1,000. The decimal point seems to move to the right by the same number of places. So 3.45 × 10 = 34.5, 3.45 × 100 = 345 and 3.45 × 1,000 = 3,450. When there are not enough digits we fill the empty places with zeros: 0.6 × 1,000 = 600. The idea is the same as with whole numbers. It is useful for metric units: 1 m = 100 cm, so 2.35 m = 2.35 × 100 = 235 cm, and 1 kg = 1,000 g, so 0.6 kg = 600 g.
Number
Thousands
Hundreds
Tens
Ones
Tenths
Hundredths
3.45
3
4
5
34.5
3
4
5
345
3
4
5
3,450
3
4
5
0
Worked examples
Work out 3.45 × 10, 3.45 × 100 and 3.45 × 1,000. The digits 3, 4 and 5 move one, two and three places left. 3.45 × 10 = 34.5, 3.45 × 100 = 345 and 3.45 × 1,000 = 3,450. In the last one a zero fills the ones place.
Work out 0.072 × 100 and 0.6 × 1,000. 0.072 × 100 = 7.2, because the digits move two places left. 0.6 × 1,000 = 600, because the 6 moves three places left and two zeros fill the gaps.
One kilogram of dates costs 12.75 LE. Ten kilograms cost 12.75 × 10 = 127.5 LE. One hundred kilograms cost 12.75 × 100 = 1,275 LE. A rope is 2.35 m long: in centimetres 2.35 × 100 = 235 cm.
Class activity
Metre to centimetre. Measure three things at home with a tape measure in metres and write each length as a decimal (for example 1.45 m). Multiply by 100 to find the length in centimetres, then check with the cm marks on the tape. Do the same with a kitchen scale: write 0.35 kg and multiply by 1,000 to get grams.
