Year 6 Maths reasoning (SATs): Decimals: thousandths, multiplying and dividing, and rounding
Part of the Year 6 Maths reasoning (SATs) fractions and decimals reasoning chapter. Chapter overview · whole chapter on one page
Decimals: thousandths, multiplying and dividing, and rounding
Rule
Each place after the decimal point is a tenth, a hundredth, a thousandth. 0.047 has 4 hundredths and 7 thousandths.
When you multiply by 10, 100 or 1000, the digits move to the left. When you divide, they move to the right.
To round, look at the digit after the rounding place: 5 or more rounds up.
Key ideas
- 0.047 = 47 thousandths, and 0.05 is bigger than 0.047.
- x 100 moves the digits two places to the left, so 4.56 x 100 = 456.
- Round to the place you are asked for, and look at the next digit.
Method. Multiply by 100 moves the digits 2 places.
- Decide which way the digits move. Multiplying by 100 moves each digit 2 places to the left; dividing moves them to the right.multiply by 100
- Move the digits. Move each digit 2 places left, and fill the gaps with zeros.4.56 becomes 456
- Write the answer. The decimal point ends in the new place.456
- Write the answer. 456
Check. 456 / 100 = 4.56. ✓
Watch out. Dividing by 100 moves the digits two places to the right, not to the left.
Method. Divide by 10 moves the digits 1 place.
- Decide which way the digits move. Multiplying by 10 moves each digit 1 place to the left; dividing moves them to the right.divide by 10
- Move the digits. Move each digit 1 place right, and fill the gaps with zeros.0.35 becomes 0.035
- Write the answer. The decimal point ends in the new place.0.035
- Write the answer. 0.035
Check. 0.035 x 10 = 0.35. ✓
Watch out. Dividing by 100 moves the digits two places to the right, not to the left.
Method. Look at the digit after the rounding place.
- Look at the digit after the hundredth place. This digit decides whether to round up or down.digit = 7
- Decide. 5 or more rounds up; 4 or less rounds down.7 is 5 or more, so round up
- Write the rounded number. Keep the digits up to the hundredth place.12.35
- Write the answer. 12.35
Check. 12.35 is the closest value to 12.3478 at this accuracy. ✓
Watch out. 2.45 to one decimal place is 2.5, because the 5 rounds up.
Watch out
Watch out. 0.5 is bigger than 0.47, even though 47 is bigger than 5. Compare the place values, not the digits alone.
Exam tip
Practice guide. Line up the decimal points before you add, subtract or compare.
Exercise 2E Practice: decimals to thousandths and rounding
Non-calculatorMethod. Find the place of the 7.
- Find the place. The 7 is in the thousandths place, the third digit after the point.thousandths
- Work out the value. 7 thousandths is 0.007.0.007
- Write the answer. 0.007
Check. 0.007 = 7 / 1000. ✓
Method. Multiply by 10 moves the digits 1 place.
- Decide which way the digits move. Multiplying by 10 moves each digit 1 place to the left; dividing moves them to the right.multiply by 10
- Move the digits. Move each digit 1 place left, and fill the gaps with zeros.6.25 becomes 62.5
- Write the answer. The decimal point ends in the new place.62.5
- Write the answer. 62.5
Check. 62.5 / 10 = 6.25. ✓
Watch out. Dividing by 100 moves the digits two places to the right, not to the left.
Method. Divide by 100 moves the digits 2 places.
- Decide which way the digits move. Multiplying by 100 moves each digit 2 places to the left; dividing moves them to the right.divide by 100
- Move the digits. Move each digit 2 places right, and fill the gaps with zeros.80.5 becomes 0.805
- Write the answer. The decimal point ends in the new place.0.805
- Write the answer. 0.805
Check. 0.805 x 100 = 80.5. ✓
Watch out. Dividing by 100 moves the digits two places to the right, not to the left.
Method. Multiply by 1000 moves the digits 3 places.
- Decide which way the digits move. Multiplying by 1000 moves each digit 3 places to the left; dividing moves them to the right.multiply by 1000
- Move the digits. Move each digit 3 places left, and fill the gaps with zeros.0.8 becomes 800
- Write the answer. The decimal point ends in the new place.800
- Write the answer. 800
Check. 800 / 1000 = 0.8. ✓
Watch out. Dividing by 100 moves the digits two places to the right, not to the left.
Method. Divide by 10 moves the digits 1 place.
- Decide which way the digits move. Multiplying by 10 moves each digit 1 place to the left; dividing moves them to the right.divide by 10
- Move the digits. Move each digit 1 place right, and fill the gaps with zeros.47.2 becomes 4.72
- Write the answer. The decimal point ends in the new place.4.72
- Write the answer. 4.72
Check. 4.72 x 10 = 47.2. ✓
Watch out. Dividing by 100 moves the digits two places to the right, not to the left.
Method. Write each number with the same number of decimal places, then compare.
- Write each with four decimal places. 0.5000, 0.0470, 0.0625, 0.4500.0.5000, 0.0470, 0.0625, 0.4500
- Compare the digits. The order from smallest is 0.0470, 0.0625, 0.4500, 0.5000.0.047, 0.0625, 0.45, 0.5
- Write the answer. 0.047, 0.0625, 0.45, 0.5
Check. 0.047 < 0.0625 < 0.45 < 0.5. ✓
Method. Look at the digit after the rounding place.
- Look at the digit after the hundredth place. This digit decides whether to round up or down.digit = 7
- Decide. 5 or more rounds up; 4 or less rounds down.7 is 5 or more, so round up
- Write the rounded number. Keep the digits up to the hundredth place.12.35
- Write the answer. 12.35
Check. 12.35 is the closest value to 12.3478 at this accuracy. ✓
Watch out. 2.45 to one decimal place is 2.5, because the 5 rounds up.
Method. Look at the digit after the rounding place.
- Look at the digit after the hundredth place. This digit decides whether to round up or down.digit = 1
- Decide. 5 or more rounds up; 4 or less rounds down.1 is 4 or less, so round down
- Write the rounded number. Keep the digits up to the hundredth place.12.05
- Write the answer. 12.05
Check. 12.05 is the closest value to 12.0519 at this accuracy. ✓
Watch out. 2.45 to one decimal place is 2.5, because the 5 rounds up.
Method. Look at the digit after the rounding place.
- Look at the digit after the tenth place. This digit decides whether to round up or down.digit = 5
- Decide. 5 or more rounds up; 4 or less rounds down.5 is 5 or more, so round up
- Write the rounded number. Keep the digits up to the tenth place.2.5
- Write the answer. 2.5
Check. 2.5 is the closest value to 2.45 at this accuracy. ✓
Watch out. 2.45 to one decimal place is 2.5, because the 5 rounds up.
Method. Look at the digit after the rounding place.
- Look at the digit after the whole number place. This digit decides whether to round up or down.digit = 6
- Decide. 5 or more rounds up; 4 or less rounds down.6 is 5 or more, so round up
- Write the rounded number. Keep the digits up to the whole number place.8
- Write the answer. 8
Check. 8 is the closest value to 7.6849 at this accuracy. ✓
Watch out. 2.45 to one decimal place is 2.5, because the 5 rounds up.
Method. Multiply by 10 by moving the digits one place to the left.
- Multiply by 10. 2.35 x 10 = 23.5.23.5
- Write with two decimal places. Money is written with two decimal places, so 23.5 becomes 23.50.23.50
- Write the answer. 23.50
Check. 23.50 / 10 = 2.35. ✓
Method. Look at the third decimal place.
- Look at the digit after the hundredths. The thousandths digit is 5, so round up.5
- Round up. 1.27 becomes 1.28.1.28
- Write the answer. 1.28
Check. 1.28 is the nearest value to 1.275 at two decimal places. ✓
Method. Test each option.
- Check each option. Test each one against the rule or the calculation.
- Tick the true ones. 0.61, 0.609 and 0.7 are all greater than 0.6.0.61, 0.609, 0.7
- Leave the others unticked. These do not match.0.59, 0.6, 0.069 are not ticked
- Write the answer. 0.61, 0.609, 0.7
Check. Each ticked option is true. ✓
Watch out. 0.6 is equal to 0.6, so it is not greater.
Method. Write both with two decimal places.
- Write both with two decimal places. 0.5 = 0.50 and 0.47 stays 0.47.0.50 and 0.47
- Compare. 50 hundredths is more than 47 hundredths.0.50 > 0.47
- Write the answer. No, because 0.5 = 0.50 and 0.50 is bigger than 0.47.
Check. 0.50 > 0.47. ✓
Method. Multiply by 1000.
- Multiply by 1000. Move the digits three places to the left.0.75 x 1000
- Write the answer. 0.75 x 1000 = 750 millilitres.750
- Write the answer. 750
Check. 750 / 1000 = 0.75. ✓
Method. Multiply the decimals, then count the decimal places.
- Multiply the digits. 6 x 1 = 6.6
- Place the decimal point. There are 2 decimal places in total, so 0.06.0.06
- Write the answer. 0.06
Check. 0.06 / 0.1 = 0.6. ✓
Watch out. Multiplying by 0.1 is the same as dividing by 10.
Method. Think about the place value of each digit.
- Multiply by 10. The 4 moves from tenths to units: 4.5 x 10 = 45.45
- Divide by 10. The 4 moves from units to tenths: 4.5 / 10 = 0.45.0.45
- Write the answer. Because x 10 moves the digits one place to the left, and / 10 moves them one place to the right.
Check. 45 / 10 = 4.5 and 0.45 x 10 = 4.5. ✓