Year 5: Comparing and ordering decimals
Part of the Year 5 decimals and percentages chapter. Chapter overview · whole chapter on one page
Comparing and ordering decimals
To compare two decimals, first write them with the same number of decimal places. Add zeros at the end: 0.6 = 0.60. Then compare the digits from the left. The first place where the digits are different decides which number is bigger.
The number line shows the decimals from 0 to 1 in tenths. Between 0.3 and 0.4 there are numbers such as 0.35, 0.36 and 0.392. The more places a decimal has, the more exact its position.
Key ideas
- Write the numbers with the same number of decimal places before you compare them.
- Compare the whole numbers first, then the tenths, the hundredths and the thousandths.
- Use > for “is greater than” and < for “is less than”. The symbol always points to the smaller number.
- Zeros at the end of a decimal do not change its value: 0.5 = 0.50 = 0.500.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Line up the place values, then compare from the left.
- Write both numbers with the same number of decimal places. Zeros at the end do not change a number. They make the columns line up.0.6 = 0.60
0.58 = 0.58 - Compare the columns from the left. The first column where the digits are different decides the answer.ones: 0 and 0, the same.
tenths: 6 and 5, so 0.6 is bigger. - Write the answer. The symbol points to the smaller number.0.6 > 0.58
Check. Read it the other way round: 0.58 < 0.6. ✓
Watch out. Do not compare the digits after the point as if they were whole numbers. 0.6 is 0.60, which is bigger than 0.58.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Write the numbers with the same number of decimal places, then compare them column by column from the left.
- Write every number with the same number of decimal places. Adding zeros at the end does not change a decimal. It lines up the place values.0.305 = 0.305
0.35 = 0.350
0.053 = 0.053 - Put them in order, smallest to largest. Start with the whole numbers. If they are the same, compare the tenths, then the hundredths, then the thousandths.0.053 < 0.305 < 0.350
- Write the answer with the original numbers. 0.053, 0.305, 0.35
Check. Read the list back. Each number is < the next one. ✓
Watch out. Do not sort by the number of digits. 0.45 and 0.405 look like 45 and 405, but 0.45 = 0.450 is the bigger number.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Line up the place values, then compare from the left.
- Write both numbers with the same number of decimal places. Zeros at the end do not change a number. They make the columns line up.4.072 = 4.072
4.7 = 4.700 - Compare the columns from the left. The first column where the digits are different decides the answer.ones: 4 and 4, the same.
tenths: 0 and 7, so 4.7 is bigger. - Write the answer. The symbol points to the smaller number.4.072 < 4.7
Check. Read it the other way round: 4.072 < 4.7. ✓
Watch out. Do not compare the digits after the point as if they were whole numbers. 0.6 is 0.60, which is bigger than 0.58.
Watch out
Do not say 0.45 is bigger than 0.5 because 45 is bigger than 5. Write 0.5 as 0.50: it is 50 hundredths, which is more than 45 hundredths. Also do not say 0.405 is bigger than 0.45 because it has more digits. 0.45 = 0.450, which is bigger.Exercise 7B Comparing and ordering decimals
Non-calculatorKey words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Line up the place values, then compare from the left.
- Write both numbers with the same number of decimal places. Zeros at the end do not change a number. They make the columns line up.0.4 = 0.4
0.6 = 0.6 - Compare the columns from the left. The first column where the digits are different decides the answer.ones: 0 and 0, the same.
tenths: 4 and 6, so 0.6 is bigger. - Write the answer. The symbol points to the smaller number.0.4 < 0.6
Check. Read it the other way round: 0.4 < 0.6. ✓
Watch out. Do not compare the digits after the point as if they were whole numbers. 0.6 is 0.60, which is bigger than 0.58.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Line up the place values, then compare from the left.
- Write both numbers with the same number of decimal places. Zeros at the end do not change a number. They make the columns line up.0.73 = 0.73
0.37 = 0.37 - Compare the columns from the left. The first column where the digits are different decides the answer.ones: 0 and 0, the same.
tenths: 7 and 3, so 0.73 is bigger. - Write the answer. The symbol points to the smaller number.0.73 > 0.37
Check. Read it the other way round: 0.37 < 0.73. ✓
Watch out. Do not compare the digits after the point as if they were whole numbers. 0.6 is 0.60, which is bigger than 0.58.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Line up the place values, then compare from the left.
- Write both numbers with the same number of decimal places. Zeros at the end do not change a number. They make the columns line up.0.8 = 0.8
0.8 = 0.8 - Compare the columns from the left. The first column where the digits are different decides the answer.ones: 0 and 0, the same.
tenths: 8 and 8, the same.
Every column is the same, so the two numbers are equal. - Write the answer. The symbol points to the smaller number.0.8 = 0.8
Check. Both numbers are the same value, written in two ways. ✓
Watch out. Do not compare the digits after the point as if they were whole numbers. 0.6 is 0.60, which is bigger than 0.58.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Line up the place values, then compare from the left.
- Write both numbers with the same number of decimal places. Zeros at the end do not change a number. They make the columns line up.0.25 = 0.250
0.205 = 0.205 - Compare the columns from the left. The first column where the digits are different decides the answer.ones: 0 and 0, the same.
tenths: 2 and 2, the same.
hundredths: 5 and 0, so 0.25 is bigger. - Write the answer. The symbol points to the smaller number.0.25 > 0.205
Check. Read it the other way round: 0.205 < 0.25. ✓
Watch out. Do not compare the digits after the point as if they were whole numbers. 0.6 is 0.60, which is bigger than 0.58.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Line up the place values, then compare from the left.
- Write both numbers with the same number of decimal places. Zeros at the end do not change a number. They make the columns line up.0.7 = 0.70
0.65 = 0.65 - Compare the columns from the left. The first column where the digits are different decides the answer.ones: 0 and 0, the same.
tenths: 7 and 6, so 0.7 is bigger. - Write the answer. The symbol points to the smaller number.0.7 > 0.65
Check. Read it the other way round: 0.65 < 0.7. ✓
Watch out. Do not compare the digits after the point as if they were whole numbers. 0.6 is 0.60, which is bigger than 0.58.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Write the numbers with the same number of decimal places, then compare them column by column from the left.
- Write every number with the same number of decimal places. Adding zeros at the end does not change a decimal. It lines up the place values.0.45 = 0.450
0.4 = 0.400
0.405 = 0.405
0.054 = 0.054 - Put them in order, smallest to largest. Start with the whole numbers. If they are the same, compare the tenths, then the hundredths, then the thousandths.0.054 < 0.400 < 0.405 < 0.450
- Write the answer with the original numbers. 0.054, 0.4, 0.405, 0.45
Check. Read the list back. Each number is < the next one. ✓
Watch out. Do not sort by the number of digits. 0.45 and 0.405 look like 45 and 405, but 0.45 = 0.450 is the bigger number.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Write the numbers with the same number of decimal places, then compare them column by column from the left.
- Write every number with the same number of decimal places. Adding zeros at the end does not change a decimal. It lines up the place values.2.5 = 2.500
2.25 = 2.250
2.205 = 2.205
2.052 = 2.052 - Put them in order, largest to smallest. Start with the whole numbers. If they are the same, compare the tenths, then the hundredths, then the thousandths.2.500 > 2.250 > 2.205 > 2.052
- Write the answer with the original numbers. 2.5, 2.25, 2.205, 2.052
Check. Read the list back. Each number is > the next one. ✓
Watch out. Do not sort by the number of digits. 0.45 and 0.405 look like 45 and 405, but 0.45 = 0.450 is the bigger number.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Try each digit in the hundredths place. Keep the numbers that are greater than 0.64 and less than 0.67.
- Try the digits near 0.64 and 0.67. Only the digits between 4 and 7 can work, so we check those.
Number Between 0.64 and 0.67? 0.64 no 0.65 yes 0.66 yes 0.67 no - Write the digits that work. Two digits give a number that is between the two.The digits are 5 and 6.
Check. 0.65 and 0.66 are both greater than 0.64 and less than 0.67. ✓
Watch out. Check the end numbers. 0.64 is not greater than 0.64, and 0.67 is not less than 0.67.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Line up the place values, then compare from the left.
- Write both numbers with the same number of decimal places. Zeros at the end do not change a number. They make the columns line up.0.509 = 0.509
0.51 = 0.510 - Compare the columns from the left. The first column where the digits are different decides the answer.ones: 0 and 0, the same.
tenths: 5 and 5, the same.
hundredths: 0 and 1, so 0.51 is bigger. - Write the answer. The symbol points to the smaller number.0.509 < 0.51
Check. Read it the other way round: 0.509 < 0.51. ✓
Watch out. Do not compare the digits after the point as if they were whole numbers. 0.6 is 0.60, which is bigger than 0.58.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Find the number exactly halfway between 0.3 and 0.4.
- Write both numbers with the same decimal places. Add a zero so that the place values line up.0.30 and 0.40
- Find the number halfway between them. Add the two numbers and divide by 2. This finds the middle.(0.30 + 0.40) ÷ 2 = 0.35
- Check on the number line. The answer should be between 0.3 and 0.4.0.3 < 0.35 < 0.4
Check. 0.35 is exactly halfway: 0.30 + 0.05 = 0.35 and 0.40 - 0.05 = 0.35. ✓
Watch out. Halfway is not 0.34 or 0.36. Use the middle of 30 and 40 hundredths.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Look for 0.35 on the number line. It is halfway between 0.3 and 0.4.
- Find 0.3 and 0.4 on the line. Each big step is 0.1, and the tenths are the marks along the line.0.3 is 3 tenths and 0.4 is 4 tenths
- Find the middle. 0.35 is halfway between 0.3 and 0.4.Point B is in the middle.
- Write the answer. B
Check. 0.35 = 35 hundredths, the middle of 30 and 40. ✓
Watch out. Halfway between two tenths is always a number with a 5 in the hundredths place.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Look for 0.9 on the number line. It is nine tenths.
- Count the tenths. Nine tenths is 0.9, which is 0.1 less than 1.0.9 = 9 tenths
- Find the mark. The mark for 0.9 is labelled D.Point D
- Write the answer. D
Check. 0.9 + 0.1 = 1. ✓
Watch out. Read the label on the point, not the nearest mark on the number line.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Compare the times column by column, from the left.
- Write every time with three decimal places. Zeros at the end do not change the time. They line up the columns.12.450 s (Ali), 12.500 s (Bea), 12.405 s (Chen)
- Compare the tenths and then the hundredths. All three have 12 whole seconds. The tenths are 4, 5 and 4, so Bea is slowest. Ali and Chen both have 4 tenths, so compare the hundredths: 5 and 0.0 hundredths is less than 5 hundredths, so Chen is faster than Ali.
- Write the answer. The smallest time is the fastest.Chen was the fastest, then Ali, then Bea.
Check. 12.405 < 12.450 < 12.500. ✓
Watch out. Do not compare 12.45 and 12.405 by the number of digits. Line up the place values.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Write the numbers with the same number of decimal places, then compare them column by column from the left.
- Write every number with the same number of decimal places. Adding zeros at the end does not change a decimal. It lines up the place values.1.25 kg = 1.250
1.052 kg = 1.052
1.5 kg = 1.500
1.205 kg = 1.205 - Put them in order, largest to smallest. Start with the whole numbers. If they are the same, compare the tenths, then the hundredths, then the thousandths.1.500 > 1.250 > 1.205 > 1.052
- Write the answer with the original numbers. 1.5 kg, 1.25 kg, 1.205 kg, 1.052 kg
Check. Read the list back. Each number is > the next one. ✓
Watch out. Do not sort by the number of digits. 0.45 and 0.405 look like 45 and 405, but 0.45 = 0.450 is the bigger number.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Test the statement with examples. One example that breaks the rule shows that “always” is wrong.
- Try a decimal with more places that is bigger. Check whether the rule works for this pair.0.25 has more places than 0.2, and 0.25 > 0.2 (0.250 > 0.200)
- Try a decimal with more places that is smaller. If one pair breaks the rule, it is not always true.0.9 has fewer places than 0.123, and 0.9 > 0.123 (0.900 > 0.123).
- Write the answer. Sometimes it is bigger and sometimes it is not, so the answer is sometimes.Sometimes
Check. Both examples are correct. ✓
Watch out. Do not decide by the number of digits. Decide by the place values.
Key words. Place value tells you what each digit is worth. We compare numbers by starting at the left and finding the first place where the digits are different. > means “is greater than”, and < means “is less than”.
Method. Write every decimal you can make, then find the one with the smallest difference from 0.5.
- List the possible decimals. Use each digit once in the tenths, hundredths and thousandths places.
Decimal Difference from 0.5 Closest? 0.527 0.027 yes 0.572 0.072 no 0.275 0.225 no 0.725 0.225 no 0.257 0.243 no 0.752 0.252 no - Find the smallest difference. The closest decimal to 0.5 is the one with the smallest difference.The smallest difference is 0.027.
- Write the answer. 0.527
Check. 0.527 is 0.027 away from 0.5. ✓
Watch out. Put the 5 in the tenths place, so the number starts 0.5. Then the other digits decide how close it is.