Year 6 Arithmetic (SATs): Comparing, ordering and rounding decimals
Part of the Year 6 Arithmetic (SATs) decimals and percentages chapter. Chapter overview · whole chapter on one page
Comparing, ordering and rounding decimals
Rule
To compare decimals, line up the decimal points and compare the digits from the left. Add zeros at the end if you need to.
To round, look at the digit just after the place you keep. If it is 5 or more, round up. If it is less, round down.
Key ideas
- Line up the decimal points, then compare from the left.
- 0.68 is bigger than 0.608, because 0.680 is bigger than 0.608.
- Round up when the next digit is 5 or more.
Method. Line up the decimal points, adding a zero to 0.68.
- Line up the decimal points. Give both numbers the same number of decimal places.0.608 and 0.680
- Compare from the left. The first place that differs decides which is bigger.digits 0 and 8
- Write the sign. The bigger number is the one with the bigger digit at the first place that differs.0.608 < 0.68
- Write the answer. <
Check. 0.608 is less than 0.680. ✓
Watch out. Do not think 608 is bigger than 68: the places are different.
Method. Write each with three decimal places, then compare the digits from the left.
- Write with three places. 0.9 = 0.900, 0.59 = 0.590, 0.6 = 0.600.0.900, 0.590, 0.600, 0.609
- Compare the tenths. Tenths: 5 for 0.590, 6 for 0.600 and 0.609, and 9 for 0.900.5 < 6 < 9
- Compare the rest. 0.600 is less than 0.609.0.59, 0.6, 0.609, 0.9
- Write the answer. 0.59, 0.6, 0.609, 0.9
Check. 0.9 is the largest because 0.900 is the biggest. ✓
Method. Keep two decimal places, then look at the next digit.
- Find the place you are rounding to. Rounding to two decimal places means keeping 2 decimal places.keep 2 places
- Look at the next digit. The digit after the place is 6. If it is 5 or more, round up; if less, round down.digit 6
- Write the rounded number. 3.4762 rounds to 3.48.3.4762 → 3.48
- Write the answer. 3.48
Check. 3.48 is nearer to 3.4762 than 3.47 is. ✓
Exercise 4B Practice: comparing, ordering and rounding
Non-calculatorMethod. Line up the decimal points and compare from the left.
- Line up the decimal points. Give both numbers the same number of decimal places.0.40 and 0.35
- Compare from the left. The first place that differs decides which is bigger.digits 4 and 3
- Write the sign. The bigger number is the one with the bigger digit at the first place that differs.0.4 > 0.35
- Write the answer. >
Check. The first place that differs gives the answer. ✓
Method. Line up the decimal points and compare from the left.
- Line up the decimal points. Give both numbers the same number of decimal places.2.07 and 2.70
- Compare from the left. The first place that differs decides which is bigger.digits 0 and 7
- Write the sign. The bigger number is the one with the bigger digit at the first place that differs.2.07 < 2.7
- Write the answer. <
Check. The first place that differs gives the answer. ✓
Method. Line up the decimal points and compare from the left.
- Line up the decimal points. Give both numbers the same number of decimal places.0.60 and 0.59
- Compare from the left. The first place that differs decides which is bigger.digits 6 and 5
- Write the sign. The bigger number is the one with the bigger digit at the first place that differs.0.6 > 0.59
- Write the answer. >
Check. The first place that differs gives the answer. ✓
Method. Line up the decimal points and compare from the left.
- Line up the decimal points. Give both numbers the same number of decimal places.5.001 and 5.010
- Compare from the left. The first place that differs decides which is bigger.digits 0 and 1
- Write the sign. The bigger number is the one with the bigger digit at the first place that differs.5.001 < 5.01
- Write the answer. <
Check. The first place that differs gives the answer. ✓
Method. Line up the decimal points and compare from the left.
- Line up the decimal points. Give both numbers the same number of decimal places.1.50 and 1.45
- Compare from the left. The first place that differs decides which is bigger.digits 5 and 4
- Write the sign. The bigger number is the one with the bigger digit at the first place that differs.1.5 > 1.45
- Write the answer. >
Check. The first place that differs gives the answer. ✓
Method. Line up the decimal points and compare from the left.
- Line up the decimal points. Give both numbers the same number of decimal places.0.08 and 0.80
- Compare from the left. The first place that differs decides which is bigger.digits 0 and 8
- Write the sign. The bigger number is the one with the bigger digit at the first place that differs.0.08 < 0.8
- Write the answer. <
Check. The first place that differs gives the answer. ✓
Method. Write each with three decimal places, then compare.
- Write with three places. 0.450, 0.400, 0.405, 0.500.0.450, 0.400, 0.405, 0.500
- Order them. 0.400 < 0.405 < 0.450 < 0.500.0.400, 0.405, 0.450, 0.500
- Write the answer. 0.4, 0.405, 0.45, 0.5
Check. 0.5 is the biggest. ✓
Method. Keep 1 decimal place, then look at the next digit.
- Find the place you are rounding to. Rounding to one decimal place means keeping 1 decimal place.keep 1 place
- Look at the next digit. The digit after the place is 3. If it is 5 or more, round up; if less, round down.digit 3
- Write the rounded number. 6.837 rounds to 6.8.6.837 → 6.8
- Write the answer. 6.8
Check. 6.8 is the nearest value with 1 decimal place. ✓
Method. Keep 2 decimal places, then look at the next digit.
- Find the place you are rounding to. Rounding to two decimal places means keeping 2 decimal places.keep 2 places
- Look at the next digit. The digit after the place is 4. If it is 5 or more, round up; if less, round down.digit 4
- Write the rounded number. 5.6249 rounds to 5.62.5.6249 → 5.62
- Write the answer. 5.62
Check. 5.62 is the nearest value with 2 decimal places. ✓
Method. Keep 2 decimal places, then look at the next digit.
- Find the place you are rounding to. Rounding to two decimal places means keeping 2 decimal places.keep 2 places
- Look at the next digit. The digit after the place is 1. If it is 5 or more, round up; if less, round down.digit 1
- Write the rounded number. 0.0715 rounds to 0.07.0.0715 → 0.07
- Write the answer. 0.07
Check. 0.07 is the nearest value with 2 decimal places. ✓
Method. Round to two decimal places, which is the nearest penny.
- Find the place you are rounding to. Rounding to the nearest penny means keeping 2 decimal places.keep 2 places
- Look at the next digit. The digit after the place is 6. If it is 5 or more, round up; if less, round down.digit 6
- Write the rounded number. 4.376 rounds to 4.38.4.376 → 4.38
- Write the answer. £4.38
Check. £4.38 is the amount to the nearest penny. ✓
Method. Round to the nearest whole number.
- Find the place you are rounding to. Rounding to the nearest whole second means keeping 0 decimal places.keep 0 places
- Look at the next digit. The digit after the place is 4. If it is 5 or more, round up; if less, round down.digit 4
- Write the rounded number. 12.4 rounds to 12.12.4 → 12
- Write the answer. 12
Check. 12.4 is nearer to 12 than to 13. ✓
Method. Look at the second decimal digit.
- Find the place you are rounding to. Rounding to one decimal place means keeping 1 decimal place.keep 1 place
- Look at the next digit. The digit after the place is 5. If it is 5 or more, round up; if less, round down.digit 5
- Write the rounded number. 2.45 rounds to 2.5.2.45 → 2.5
- Write the answer. 2.5
Check. The rule for halves: 5 rounds up, so 2.5. ✓
Method. Look at the digit after the place you are rounding to.
- Look at the digit. The second decimal digit is 5, so round up.5 → up
- Round the number. 2.45 rounds to 2.5.2.5
- Write the answer. No, 2.45 rounds to 2.5 to one decimal place, because the second digit 5 means round up.
Check. 2.4 would only be right if the digit were 4 or less. ✓