Step-by-step Maths Level 5: Equal decimals, comparing and ordering
Part of the Step-by-step Maths Level 5 decimals to tenths and hundredths chapter. Chapter overview · whole chapter on one page
Equal decimals, comparing and ordering
Adding a zero at the end of a decimal does not change its value. 0.5 = 0.50, because 5 tenths is the same as 50 hundredths.
To compare decimals, look at the whole numbers, then the tenths, then the hundredths.
Key ideas
- A zero at the end does not change the value: 0.5 = 0.50.
- Compare the whole numbers first, then tenths, then hundredths.
- Order from the smallest by comparing each place.
Method. A zero at the end of a decimal does not change its value.
- Add a zero at the end. Adding a zero after the last digit does not change the value.0.5 = 0.50
- Compare the two numbers. The tenths digit and the zero in the hundredths are both empty places.0.50 = 0.5
- Write the answer. They are equal; the zero only shows that there are no hundredths.0.50
Check. Check: 5/10 = 50/100.
Watch out. 0.5 and 0.50 are equal. The zero at the end does not make the number bigger.
Method. Compare the digits from the left: whole numbers, then tenths, then hundredths.
- Compare the whole numbers. The bigger whole number is the bigger decimal.0 and 0
- Compare the tenths. If the whole numbers match, the tenths decide.4 and 5 tenths
- Compare the hundredths. If the tenths also match, the hundredths decide.5 and 0 hundredths
- Choose the greater number. This is the number with the larger digit in the first place they differ.0.50
Check. Check: 0.50 is 50 hundredths and 0.45 is 45 hundredths.
Watch out. Do not think 0.45 is bigger than 0.5 because 45 is bigger than 5. Compare the tenths first.
Method. Compare the whole numbers, then the tenths, then the hundredths.
- Compare the whole numbers. Put the smallest whole number first.0, 0, 0, 4
- Compare the tenths and hundredths. Use the next places to put the rest in order.0.47, 0.04, 0.50, 4.05
- Write the list smallest first. Check each pair in order.0.04, 0.47, 0.50, 4.05
Check. Check: each number is smaller than the one after it.
Watch out. Do not order by the number of digits. Compare the places from the left.
Watch out
Watch out. 0.45 is less than 0.5, even though 45 is more than 5. Compare the tenths first.
Exam tip
Grown-up tip. Ask: “Which is greater, 0.6 or 0.58?” Then ask why the tenths decide before the hundredths.
Exercise 7C Practice: equal decimals, comparing and ordering
Non-calculatorMethod. A zero at the end of a decimal does not change its value.
- Add a zero at the end. Adding a zero after the last digit does not change the value.5.6 = 5.60
- Compare the two numbers. The tenths digit and the zero in the hundredths are both empty places.5.60 = 5.6
- Write the answer. They are equal; the zero only shows that there are no hundredths.5.60
Check. Check: 56/10 = 560/100.
Watch out. 0.5 and 0.50 are equal. The zero at the end does not make the number bigger.
Method. Compare the digits from the left: whole numbers, then tenths, then hundredths.
- Compare the whole numbers. The bigger whole number is the bigger decimal.5 and 6
- Compare the tenths. If the whole numbers match, the tenths decide.9 and 7 tenths
- Compare the hundredths. If the tenths also match, the hundredths decide.4 and 3 hundredths
- Choose the greater number. This is the number with the larger digit in the first place they differ.6.73
Check. Check: 6.73 is 673 hundredths and 5.94 is 594 hundredths.
Watch out. Do not think 0.45 is bigger than 0.5 because 45 is bigger than 5. Compare the tenths first.
Method. Compare the digits from the left: whole numbers, then tenths, then hundredths.
- Compare the whole numbers. The bigger whole number is the bigger decimal.6 and 2
- Compare the tenths. If the whole numbers match, the tenths decide.2 and 7 tenths
- Compare the hundredths. If the tenths also match, the hundredths decide.3 and 9 hundredths
- Choose the greater number. This is the number with the larger digit in the first place they differ.6.23
Check. Check: 6.23 is 623 hundredths and 2.79 is 279 hundredths.
Watch out. Do not think 0.45 is bigger than 0.5 because 45 is bigger than 5. Compare the tenths first.
Method. Compare the whole numbers, then the tenths, then the hundredths.
- Compare the whole numbers. Put the smallest whole number first.6, 2, 3, 9
- Compare the tenths and hundredths. Use the next places to put the rest in order.6.97, 2.74, 3.52, 9.82
- Write the list smallest first. Check each pair in order.2.74, 3.52, 6.97, 9.82
Check. Check: each number is smaller than the one after it.
Watch out. Do not order by the number of digits. Compare the places from the left.
Method. Compare the whole numbers, then the tenths, then the hundredths.
- Compare the whole numbers. Put the smallest whole number first.8, 4, 8, 4
- Compare the tenths and hundredths. Use the next places to put the rest in order.8.29, 4.48, 8.84, 4.20
- Write the list smallest first. Check each pair in order.4.20, 4.48, 8.29, 8.84
Check. Check: each number is smaller than the one after it.
Watch out. Do not order by the number of digits. Compare the places from the left.
Method. Compare the digits from the left: whole numbers, then tenths, then hundredths.
- Compare the whole numbers. The bigger whole number is the bigger decimal.3 and 3
- Compare the tenths. If the whole numbers match, the tenths decide.6 and 4 tenths
- Compare the hundredths. If the tenths also match, the hundredths decide.8 and 1 hundredths
- Choose the greater number. This is the number with the larger digit in the first place they differ.3.68
Check. Check: 3.68 is 368 hundredths and 3.41 is 341 hundredths.
Watch out. Do not think 0.45 is bigger than 0.5 because 45 is bigger than 5. Compare the tenths first.
Method. Compare the whole numbers, then the tenths, then the hundredths.
- Compare the whole numbers. Put the smallest whole number first.5, 7, 8, 7
- Compare the tenths and hundredths. Use the next places to put the rest in order.5.60, 7.33, 8.61, 7.56
- Write the list smallest first. Check each pair in order.5.60, 7.33, 7.56, 8.61
Check. Check: each number is smaller than the one after it.
Watch out. Do not order by the number of digits. Compare the places from the left.
Method. A zero at the end of a decimal does not change its value.
- Add a zero at the end. Adding a zero after the last digit does not change the value.9.1 = 9.10
- Compare the two numbers. The tenths digit and the zero in the hundredths are both empty places.9.10 = 9.1
- Write the answer. They are equal; the zero only shows that there are no hundredths.9.10
Check. Check: 91/10 = 910/100.
Watch out. 0.5 and 0.50 are equal. The zero at the end does not make the number bigger.
Method. Compare the whole numbers, then the tenths, then the hundredths.
- Compare the whole numbers. Put the smallest whole number first.2, 6, 8, 6
- Compare the tenths and hundredths. Use the next places to put the rest in order.2.13, 6.78, 8.67, 6.07
- Write the list smallest first. Check each pair in order.2.13, 6.07, 6.78, 8.67
Check. Check: each number is smaller than the one after it.
Watch out. Do not order by the number of digits. Compare the places from the left.
Method. Compare the digits from the left: whole numbers, then tenths, then hundredths.
- Compare the whole numbers. The bigger whole number is the bigger decimal.8 and 3
- Compare the tenths. If the whole numbers match, the tenths decide.1 and 1 tenths
- Compare the hundredths. If the tenths also match, the hundredths decide.1 and 2 hundredths
- Choose the greater number. This is the number with the larger digit in the first place they differ.8.11
Check. Check: 8.11 is 811 hundredths and 3.12 is 312 hundredths.
Watch out. Do not think 0.45 is bigger than 0.5 because 45 is bigger than 5. Compare the tenths first.
Method. Compare the whole numbers, then the tenths, then the hundredths.
- Compare the whole numbers. Put the smallest whole number first.6, 4, 2, 4
- Compare the tenths and hundredths. Use the next places to put the rest in order.6.87, 4.11, 2.99, 4.08
- Write the list smallest first. Check each pair in order.2.99, 4.08, 4.11, 6.87
Check. Check: each number is smaller than the one after it.
Watch out. Do not order by the number of digits. Compare the places from the left.
Method. Compare the digits from the left: whole numbers, then tenths, then hundredths.
- Compare the whole numbers. The bigger whole number is the bigger decimal.6 and 8
- Compare the tenths. If the whole numbers match, the tenths decide.4 and 4 tenths
- Compare the hundredths. If the tenths also match, the hundredths decide.3 and 3 hundredths
- Choose the greater number. This is the number with the larger digit in the first place they differ.8.43
Check. Check: 8.43 is 843 hundredths and 6.43 is 643 hundredths.
Watch out. Do not think 0.45 is bigger than 0.5 because 45 is bigger than 5. Compare the tenths first.
Method. Compare the digits from the left: whole numbers, then tenths, then hundredths.
- Compare the whole numbers. The bigger whole number is the bigger decimal.1 and 3
- Compare the tenths. If the whole numbers match, the tenths decide.9 and 2 tenths
- Compare the hundredths. If the tenths also match, the hundredths decide.1 and 3 hundredths
- Choose the greater number. This is the number with the larger digit in the first place they differ.3.23
Check. Check: 3.23 is 323 hundredths and 1.91 is 191 hundredths.
Watch out. Do not think 0.45 is bigger than 0.5 because 45 is bigger than 5. Compare the tenths first.
Method. Compare the digits from the left: whole numbers, then tenths, then hundredths.
- Compare the whole numbers. The bigger whole number is the bigger decimal.4 and 6
- Compare the tenths. If the whole numbers match, the tenths decide.2 and 6 tenths
- Compare the hundredths. If the tenths also match, the hundredths decide.9 and 8 hundredths
- Choose the greater number. This is the number with the larger digit in the first place they differ.6.68
Check. Check: 6.68 is 668 hundredths and 4.29 is 429 hundredths.
Watch out. Do not think 0.45 is bigger than 0.5 because 45 is bigger than 5. Compare the tenths first.
Method. Compare the digits from the left: whole numbers, then tenths, then hundredths.
- Compare the whole numbers. The bigger whole number is the bigger decimal.8 and 5
- Compare the tenths. If the whole numbers match, the tenths decide.1 and 2 tenths
- Compare the hundredths. If the tenths also match, the hundredths decide.4 and 5 hundredths
- Choose the greater number. This is the number with the larger digit in the first place they differ.8.14
Check. Check: 8.14 is 814 hundredths and 5.25 is 525 hundredths.
Watch out. Do not think 0.45 is bigger than 0.5 because 45 is bigger than 5. Compare the tenths first.
Method. Compare the digits from the left: whole numbers, then tenths, then hundredths.
- Compare the whole numbers. The bigger whole number is the bigger decimal.2 and 5
- Compare the tenths. If the whole numbers match, the tenths decide.3 and 2 tenths
- Compare the hundredths. If the tenths also match, the hundredths decide.4 and 7 hundredths
- Choose the greater number. This is the number with the larger digit in the first place they differ.5.27
Check. Check: 5.27 is 527 hundredths and 2.34 is 234 hundredths.
Watch out. Do not think 0.45 is bigger than 0.5 because 45 is bigger than 5. Compare the tenths first.