Step-by-step Maths Level 3: Changing units, and comparing lengths and masses
Part of the Step-by-step Maths Level 3 length and mass chapter. Chapter overview · whole chapter on one page
Changing units, and comparing lengths and masses
100 cm is the same as 1 m. 1000 g is the same as 1 kg.
To compare two measures, change them to the same unit first. Then compare the numbers.
Key ideas
- 100 cm = 1 m.
- 1000 g = 1 kg.
- Change to the same unit before comparing.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Remember the rule. 1 m is 100 cm.1 m = 100 cm
- Multiply the metres by 100. There are 3 metres, so 3 lots of 100.3 × 100 = 300
- Write the answer in centimetres. This is the length in centimetres.300 cm
Check. Divide 300 cm by 100 to get 3 m.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Find the number of whole kilograms. 1000 g make 1 kg.4250 ÷ 1000 = 4 rem 250
- Write the grams that are left. The rest are grams.4 kg and 250 g
- Write the answer. Use kilograms and grams.4 kg 250 g
Check. Add back: 4 kg + 250 g = 4250 g.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 100 cm = 1 m, so change both to the smaller unit.2 m = 200 cm, 2 m 50 cm = 250 cm
- Compare the numbers. Compare the bigger numbers.200 cm and 250 cm
- Write the sign. 2 m is less than 2 m 50 cm.<
Check. 2 m < 2 m 50 cm is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Watch out
Watch out. 2 m is more than 150 cm. Do not compare 2 with 150 directly, because the units are different.
Exam tip
Grown-up tip. Use a metre stick or a 1 kg bag of flour to see the size of the units, and ask which is more.
Exercise 9C Practice: changing units and comparing
Non-calculatorMethod. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Remember the rule. 1 m is 100 cm.1 m = 100 cm
- Multiply the metres by 100. There are 2 metres, so 2 lots of 100.2 × 100 = 200
- Write the answer in centimetres. This is the length in centimetres.200 cm
Check. Divide 200 cm by 100 to get 2 m.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Find the number of whole kilograms. 1000 g make 1 kg.2250 ÷ 1000 = 2 rem 250
- Write the grams that are left. The rest are grams.2 kg and 250 g
- Write the answer. Use kilograms and grams.2 kg 250 g
Check. Add back: 2 kg + 250 g = 2250 g.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Remember the rule. 1 kg is 1000 g.1 kg = 1000 g
- Multiply the kilograms by 1000. There are 2 kilograms, so 2 lots of 1000.2 × 1000 = 2000
- Write the answer in grams. This is the mass in grams.2000 g
Check. Divide 2000 g by 1000 to get 2 kg.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Remember the rule. 1 kg is 1000 g.1 kg = 1000 g
- Multiply the kilograms by 1000. There are 3 kilograms, so 3 lots of 1000.3 × 1000 = 3000
- Write the answer in grams. This is the mass in grams.3000 g
Check. Divide 3000 g by 1000 to get 3 kg.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Find the number of whole kilograms. 1000 g make 1 kg.3250 ÷ 1000 = 3 rem 250
- Write the grams that are left. The rest are grams.3 kg and 250 g
- Write the answer. Use kilograms and grams.3 kg 250 g
Check. Add back: 3 kg + 250 g = 3250 g.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Find the number of whole kilograms. 1000 g make 1 kg.8250 ÷ 1000 = 8 rem 250
- Write the grams that are left. The rest are grams.8 kg and 250 g
- Write the answer. Use kilograms and grams.8 kg 250 g
Check. Add back: 8 kg + 250 g = 8250 g.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Find the number of whole kilograms. 1000 g make 1 kg.1250 ÷ 1000 = 1 rem 250
- Write the grams that are left. The rest are grams.1 kg and 250 g
- Write the answer. Use kilograms and grams.1 kg 250 g
Check. Add back: 1 kg + 250 g = 1250 g.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Remember the rule. 1 kg is 1000 g.1 kg = 1000 g
- Multiply the kilograms by 1000. There are 6 kilograms, so 6 lots of 1000.6 × 1000 = 6000
- Write the answer in grams. This is the mass in grams.6000 g
Check. Divide 6000 g by 1000 to get 6 kg.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 100 cm = 1 m, so change both to the smaller unit.3 m 26 cm = 326 cm, 19 cm = 19 cm
- Compare the numbers. Compare the bigger numbers.326 cm and 19 cm
- Write the sign. 3 m 26 cm is more than 19 cm.>
Check. 3 m 26 cm > 19 cm is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 100 cm = 1 m, so change both to the smaller unit.1 m = 100 cm, 3 m 50 cm = 350 cm
- Compare the numbers. Compare the bigger numbers.100 cm and 350 cm
- Write the sign. 1 m is less than 3 m 50 cm.<
Check. 1 m < 3 m 50 cm is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 1000 g = 1 kg, so change both to the smaller unit.2 kg 250 g = 2250 g, 3 kg = 3000 g
- Compare the numbers. Compare the bigger numbers.2250 g and 3000 g
- Write the sign. 2 kg 250 g is less than 3 kg.<
Check. 2 kg 250 g < 3 kg is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 100 cm = 1 m, so change both to the smaller unit.4 m 51 cm = 451 cm, 2 m = 200 cm
- Compare the numbers. Compare the bigger numbers.451 cm and 200 cm
- Write the sign. 4 m 51 cm is more than 2 m.>
Check. 4 m 51 cm > 2 m is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 100 cm = 1 m, so change both to the smaller unit.4 m 19 cm = 419 cm, 2 m 9 cm = 209 cm
- Compare the numbers. Compare the bigger numbers.419 cm and 209 cm
- Write the sign. 4 m 19 cm is more than 2 m 9 cm.>
Check. 4 m 19 cm > 2 m 9 cm is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 100 cm = 1 m, so change both to the smaller unit.2 m 17 cm = 217 cm, 2 m 23 cm = 223 cm
- Compare the numbers. Compare the bigger numbers.217 cm and 223 cm
- Write the sign. 2 m 17 cm is less than 2 m 23 cm.<
Check. 2 m 17 cm < 2 m 23 cm is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 1000 g = 1 kg, so change both to the smaller unit.2 kg 500 g = 2500 g, 100 g = 100 g
- Compare the numbers. Compare the bigger numbers.2500 g and 100 g
- Write the sign. 2 kg 500 g is more than 100 g.>
Check. 2 kg 500 g > 100 g is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 1000 g = 1 kg, so change both to the smaller unit.4 kg = 4000 g, 1 kg 500 g = 1500 g
- Compare the numbers. Compare the bigger numbers.4000 g and 1500 g
- Write the sign. 4 kg is more than 1 kg 500 g.>
Check. 4 kg > 1 kg 500 g is true.
Watch out. Change to the smaller unit first. Then compare the numbers.