Year 6 Arithmetic (SATs): Decimals as fractions and place value to three places
Part of the Year 6 Arithmetic (SATs) decimals and percentages chapter. Chapter overview · whole chapter on one page
Decimals as fractions and place value to three places
Rule
Each decimal place is a column: tenths (0.1), hundredths (0.01) and thousandths (0.001). A decimal can be written as a fraction over 10, 100 or 1000: 0.71 = 71/100.
Multiplying by 10, 100 or 1000 moves the digits to the left; dividing moves them to the right. For the full work on decimals, read Year 6 maths, chapter 4.
Key ideas
- 0.71 = 71/100: the number of decimal places sets the bottom number.
- Thousandths are three places after the point: 0.005 = 5/1000.
- Multiply by 100 moves the digits two places to the left.
- Divide by 1000 moves the digits three places to the right.
Method. Count the decimal places, then use that many zeros on the bottom.
- Count the places. 0.71 has two decimal places.two places
- Write the digits over the matching power of 10. Two places means 100 on the bottom.71/100
- Check it cannot be simplified. 71 is a prime number, so the fraction is simplest.71/100
- Write the answer. 71/100
Check. 71 ÷ 100 = 0.71. ✓
Method. Find the column of the 7, then write its value.
- Find the column. The 7 is the second digit after the point, so it is in the hundredths column.hundredths
- Write the value. 7 hundredths is 7 ÷ 100.7 × 0.01 = 0.07
- Write the answer. The value of the 7 is 0.07.0.07
- Write the answer. 0.07
Check. 4.572 = 4 + 0.5 + 0.07 + 0.002. ✓
Method. Three places means the bottom is 1000.
- Write over 1000. 0.005 has three decimal places, so the bottom is 1000.5/1000
- Simplify. Divide the top and bottom by 5.5/1000 = 1/200
- Check. 1/200 = 0.005.0.005 = 1/200
- Write the answer. 1/200
Check. 200 × 0.005 = 1. ✓
Exercise 4A Practice: decimals as fractions and place value
Non-calculatorMethod. Write over 10.
- Write over the power of 10. 0.3 has 1 decimal place.0.3
- Simplify. Divide the top and bottom by their highest common factor.3/10
- Write the answer. 3/10
Check. 3/10 = 0.3. ✓
Method. Write over 100, then simplify by 5.
- Write over the power of 10. 0.45 has 2 decimal places.0.45
- Simplify. Divide the top and bottom by their highest common factor.9/20
- Write the answer. 9/20
Check. 9/20 = 0.45. ✓
Method. Write over 1000, then simplify by 125.
- Write over the power of 10. 0.125 has 3 decimal places.0.125
- Simplify. Divide the top and bottom by their highest common factor.1/8
- Write the answer. 1/8
Check. 1/8 = 0.125. ✓
Method. Write over 10, then simplify by 2.
- Write over the power of 10. 2.6 has 1 decimal place.2.6
- Simplify. Divide the top and bottom by their highest common factor.13/5
- Write the answer. 13/5
Check. 13/5 = 2.6. ✓
Method. The 6 is in the hundredths column.
- Find the column. The 6 is in the hundredths column.hundredths
- Write the value. 6 hundredths is 6 ÷ 100.6 × 0.01 = 0.06
- Write the answer. 0.06
Check. Check the other digits: the number is 3.961. ✓
Method. The 4 is in the hundredths column.
- Find the column. The 4 is in the hundredths column.hundredths
- Write the value. 4 hundredths is 4 ÷ 100.4 × 0.01 = 0.04
- Write the answer. 0.04
Check. Check the other digits: the number is 0.248. ✓
Method. Find the thousandths column.
- Find the column. The 8 is the third digit after the point, so it is in the thousandths column.thousandths
- Write the value. 8 thousandths is 0.008.0.008
- Write the answer. 0.008
Check. 0.05 + 0.008 = 0.058. ✓
Method. Multiply by 100 moves the digits two places to the left.
- Move each digit two places left. The 4 moves to the units column and the 7 to the tenths.0.047 → 4.7
- Write the answer. 4.7
Check. 4.7 ÷ 100 = 0.047. ✓
Method. Multiply by 1000 moves the digits three places to the left.
- Move each digit three places left. The 5 moves to the tens and the 6 to the units.0.056 → 56
- Write the answer. 56
Check. 56 ÷ 1000 = 0.056. ✓
Method. Divide by 10 moves each digit one place to the right.
- Move each digit one place right. The 3 moves to the tenths and the 5 to the hundredths.3.56 → 0.356
- Write the answer. 0.356
Check. 0.356 × 10 = 3.56. ✓
Method. Divide by 100 moves each digit two places to the right.
- Move each digit two places right. The 4 moves to the hundredths and the 8 to the thousandths.4.8 → 0.048
- Write the answer. 0.048
Check. 0.048 × 100 = 4.8. ✓
Method. Count the places after the decimal point.
- Count the places. Tenths 3, hundredths 1, thousandths 7.3, 1, 7
- Write the answer. 7
Check. 4.317 = 4 + 0.3 + 0.01 + 0.007. ✓
Method. One kilogram is 1000 grams, so multiply by 1000.
- Multiply by 1000. 1.650 × 1000 moves the digits three places left.1.650 → 1650
- Read the answer in grams. The answer is in grams.1650 g
- Write the answer. 1650
Check. 1650 ÷ 1000 = 1.65 kg. ✓
Method. Write both as fractions.
- Write 0.7 as a fraction. 0.7 = 7/10.7/10
- Write 0.70 as a fraction. 0.70 = 70/100, which simplifies to 7/10.70/100 = 7/10
- Write the answer. No, 0.70 and 0.7 have the same value because the zero at the end is not worth anything.
Check. Both are 7/10. ✓
Method. Write 0.125 over 1000, then simplify.
- Write over 1000. 0.125 = 125/1000.125/1000
- Simplify. Divide the top and bottom by 125.125/1000 = 1/8
- Write the answer. 1/8
Check. Ali is wrong: 1/125 is 0.008. ✓